There are some advantages to drawing the boundaries of cities fairly broadly - it allows an easy coordination of transportation policy, it ensures that most people who work in the city also live there (and vice-versa).
The question of why a certain municipality did or did not merge with a number of surrounding villages typically depends on how the country in question handles local government. In France, going down from the Republic at-large there are regions, dpartements and ultimately cities/towns/villages. Most of the Paris urban area is in the region le de France which is made up of multiple dpartements; one of these (number 75) is the city of Paris (or traditionally Seine as per its location in the alphabetical index). Interestingly, this dpartement used to be larger (and contain multiple municipalities) but was split into four dpartements (Hauts-de-Seine, Seine-Saint-Denis and Val-de-Marne alongside Paris proper) in 1968. I suspect that the central government did not want too much of an imbalance between the main city/dpartement and the areas surrounding it; and maybe also population distributions or importance of dpartements/regions on a national level was a concern.
In Germany, the cities of Berlin and Hamburg were enlarged in the interwar period by national laws. After the Second World War, many of the original state boundaries (or province boundaries in case of the provinces of Prussia which was dissolved) were kept and the new German states would, where possible, be made up of entire former states. Some boundaries have shifted, some states have merged but Hamburg and Berlin remained unchanged. However, they (and Bremen) are special municipalities in that they themselves are at the level of a state. This means, the mayors of Hamburg, Bremen and Berlin are equal in rank to the minister presidents of e.g. Bavaria and North-Rhine Westfalia but above the mayors of e.g. Munich or Cologne. The city government has state-level and municipality-level duties but I believe some of them are delegated to borough governments.
Munich is larger than Bremen (but smaller than Hamburg and Berlin), yet it is fully contained within the state of Bavaria whose capital it is. Cologne, the fourth-largest city in Germany is part of North-Rhine Westfalia but not the state capital. These two cities (and many, many others) are still special in that they are not contained in a Landkreis (a regional governing area like English counties or French dpartements); they are Kreis-free cities. However, this still puts them on the same level as much smaller Kreis-free cities such as Kaufbeuren.
With respect to Munich, the Bavarian state is divided into regions (Regierungsbezirke) and it was recently discussed whether Munich should become its own region (it is currently in the region of Upper Bavaria). However, that discussion seems to be going nowhere. Other large cities of Germany are probably going to stay where they are and even a merger of Bremen and the surrouding state of Lower Saxony (i.e. the opposite direction; but making sense considering how much smaller Bremen is) is probably not going to happen any time soon.
I suspect that the city limits of Paris are mostly a matter of historical path dependency. Cities in Europe (and many of the older cities founded in the original thirteen US states) were often created by coalescing a number of independent villages that rose up around some important resource or feature: a port, a military fortification, an aqueduct or other construction, etc. The villages arose because people wanted to be as close to the resource as possible while still maintaining enough open land for productive agriculture, but as populations increase, villages grow out over the agricultural land until they merge together. Within these new cities, the old villages still maintain a degree of political sovereignty, and often resist any incorporation that would rob them of that independent identity. Back in the day, the central fortification likely marked the original 'Paris,' with all the other territory of the modern city being composed of agricultural villages that supplied the military compound with food and supplies; Now they've all grown together, but that central region still considers itself 'Paris' in exclusion to the expanded metropolis.
Berlin is unique among European cities in that in the aftermath of WWII the city was extensively damaged and then split in two between different nations. The borders of the city of Berlin became a matter of international concern, and that high-level focus erased most of the effects of local/historical politics. Had WWII not happened, Berlin would likely still have the 'coalesced villages' structure typical of other cities, and that 3.75 million figure would be split up among various regions, much the way that the population of Manhattan is often contrasted with the population of New York City.
As Jontia pointed out, Paris is one departement, out of 98? 99? in France. At 2+ million inhabitants it is already a big department and doesn't need to be any more powerful (that's a matter of opinion of course, as Paris likes to think it's the only city that matters in France). What you think of as a natural unit of government of a greater urban area is taken care of by its membership of the Ile-de-France region, which does cover the neighboring departments. For example, public transport, is coordinated by this body, which does cover the suburbs.
The other bit is that Paris proper is sometimes referred to as Paris intra muros (French), i.e. Paris-within-the-walls. Now, I am not totally sure where the walls (French) went and when they were taken out, but as far as I understand, they were roughly located where the peripherique ring road is and therefore the city limits are basically where the walls used to be + 2 of the neighboring parks.
I have a ritual when in Paris. I ask my taxi driver to take me around the Arc de Triomphe two times. My cabbie plunges into the grand traffic circle where a dozen boulevards converge on this mightiest of triumphal arches. Like referees at gladiator camp, traffic cops are stationed at each entrance to this traffic circus, letting in bursts of eager cars. Each time, being immersed in the crazy traffic with my cabbie so in control makes me laugh out loud.
In the mid-19th century, Baron Haussmann set out to make Paris the grandest city in Europe. The 12 arterials that radiate from the Arc de Triomphe were part of his master plan: the creation of a series of major boulevards, intersecting at diagonals with monuments as centerpieces (such as the Arc de Triomphe). As we zip around the circle, it's obvious that Haussmann's plan did not anticipate the automobile.
My cabbie explains to me, "If there is an accident here, each driver is considered equally at fault. This is the only place in Paris where the accidents are not judged. No matter what the circumstances, insurance companies split the costs fifty-fifty. In Paris, a good driver gets only scratches, not dents."
While we're momentarily stalled on the inside lane, I pay and hop out. The cabbie drives away, leaving me feeling small under Europe's ultimate arch and at the top of the Champs-Elyses, its ultimate boulevard.
Each visit here reminds me of the greatness of France. As marble Lady Liberties scramble up the arch Napoleon ordered built, heroically thrusting their swords and shrieking at the traffic, all of Paris seems drawn into this whirlpool.
The Arc de Triomphe affords a great Paris view, but only to those who earn it by climbing its 284 steps. Begun in 1806, the arch was intended to honor Napoleon's soldiers, who, in spite of being vastly outnumbered by the Austrians, scored a remarkable victory at the battle of Austerlitz. Napoleon died long before the arch was completed. But it was finished in time for his posthumous homecoming in 1840. Nineteen years after he died in exile on St. Helena, his remains were carried in a grand parade underneath his grand arch.
The Arc de Triomphe is dedicated to the glory of all French armies. Like its Roman ancestors, this arch has served as a parade gateway for triumphal armies (French or foe) and the stage for important ceremonies. From 1940 to 1944, a large swastika flew from here as Nazis goose-stepped daily down the Champs-Elyses. Allied troops marched triumphantly under this arch in August 1944.
Climbing to the top of the arch is like summiting Paris. From this historic perch you look down along the huge axis that shoots like an arrow all the way from the Louvre, up the Champs-Elyses, through the arch, then straight down Avenue de la Grande-Arme to a forest of distant skyscrapers around an even bigger modern arch in suburban La Dfense.
The Turgot map of Paris (French: Plan de Turgot) is a highly accurate and detailed map of the city of Paris, France, as it existed in the 1730s. The map was commissioned by Parisian municipality chief Michel-tienne Turgot, drawn up by surveyor Louis Bretez, and engraved by Claude Lucas.
The Turgot map was published in 1739 as an atlas of twenty non-overlapping sectional bird's-eye-view maps (at a scale of approximately 1:400) in isometric perspective toward the southeast. Additionally, there is one simplified general map with a four-by-five grid showing the layout of the twenty sectional maps. The atlas covers an area approximately corresponding to the first eleven of the modern-day arrondissements of Paris. Each sectional map consists of double-facing sheets and is 80 cm (31 in) wide; the first row is 48 cm (19 in) high, while the remaining rows are 50 cm (20 in) high. The assembled map is 250.5 cm (98.5 in) in height and 322.5 cm (127 in) in width.[1] Turgot's map has been described as "the first all-comprising graphical inventory of the capital, down to the last orchard and tree, detailing every house and naming even the most modest cul-de-sac".[2]
In 1734, Michel-tienne Turgot, the chief of the municipality of Paris as provost of the city's merchants, decided to promote the reputation of Paris for Parisian, provincial and foreign elites by commissioning a new map of the city. He asked Louis Bretez, a member of the Acadmie royale de peinture et de sculpture (Royal Academy of Painting and Sculpture) and professor of perspective, to draw up a map of Paris and its suburbs. By contract, Turgot requested a very faithful reproduction with great accuracy. Bretez was allowed to enter mansions, houses and gardens to take measurements and draw pictures, and worked on the project from 1734 to 1736.[3]