Here is Marshall K. Kirk's rough translation of the most relevant part
of Settipani's /Les ancêtres de Charlemagne/ (1989), namely his
treatment of Bertha of Prum (pp. 29-31):
13 Bertha of Prum, foundress of the abbey of Prum 721.
[list of sources and a bibliography including M. Chaume, E. Hlawitschka,
S. de Vajay, N. Gauthier, M. Werner, and C. Bouchard]
Bertrade or Bertha made in 721 an important donation of lands inherited
from her ancestors for the foundation of the monastery of Prum. This
donation intervenes for the repose of deceased sons, and it is
countersigned by her surviving son, Caribert, as well as by three viri
magnifici: Bernier, Rolande, and Thierry.
In order to retrieve the ancestors of Bertha, we dispose of two
elements: onomastics, and the identification of her properties.
On the level of nomenclature, the names of Bertha, Caribert her son,
Thierry her relative, are all characteristic of the Merovingian dynasty.
This is the reason for which the majority of historians, especially in
France, don't doubt that Bertha belonged to this dynasty. It remains,
however, difficult to specify in what fashion to state this. That
Thierry and the two other subscribers of the charter, Bernier and
Rolande, made part of the close kin of Bertha and of her son Caribert,
is what emerges fully from analysis of the testament of Fulrad of
Sain-Denis and of the family of Saint William of Gellone. Fulrad names,
as co-proprietors of numerous goods which he'd bought from them,
Caribert and Thierry, without any doubt the two individuals of the
charter of Prum. If they were co-proprietors, then they had, in quite a
close degree, a common ancestor. Saint William (d. 804), for his part,
had as children a Thierry, a Garnier, a Rolande, and a Caribert, while
one of his sisters was called Bertha.
Above all, one notes the fact that in 751, Pepin the Short and his
spouse Bertha, granddaughter of our subject, had in common two
properties, Rommersheim and Rheinbach, of which they each held a moiety
from their respective fathers, Charles Martel and Caribert of Laon. That
signifies that Charles Martel and Caribert were directly related and
that they had therefore inherited from the same personage a moiety of
these two villas. For Caribert, it is known, thanks to the act of
foundation of Prum, that Rommersheim came to him from his mother, and
thus that it is by way of her that the sought-for alliance passes. E.
HLAWITSCHKA has, moreover, excluded -- with reason -- the possibility
that Bertha obtained this land from her spouse, since she expressly
declares that she is giving goods which came to her from her ancestors.
There remain only three options: Bertha was the sister (or cousin) of
Pepin, father of Charles; or of Alpaide, his mother; or perhaps of
Plectrude, first spouse of Pepin, from whom Charles had inherited the
property at the deaths of the last descendants of this last. E.
HLAWITSCHKA, who has weighed the various solutions at length, concludes
that one can throw out the idea that Bertha was Pepin's sister. In this
case, in fact, Bertha would have been a Pepinid, which is ruled out by
the silence of the sources, and above all by the fact that the degree of
consanguinity between Pepin the Short and his spouse would thus have
been prohibited. The two other possibilities are equiprobable, the first
having, nevertheless, the advantage of simplicity, unless another
argument comes along to reinforce the second. Now, this is precisely
what happens. The second subscriber of the donation of Prum is the noble
Rolande, namesake of a sister of Plectrude. Whether we're talking about
a single person or two related homonyms is of small import. In either
case, Bertha was surely related to Plectrude. In order to justify her
having divided with the latter a moiety of Rommersheim and Rheinbach, it
is necessary that they were cousins german or more probably sisters.
This is the demonstration generally followed by the most recent authors,
notably N. GAUTHIER.
The trouble is, that this solution makes no use at all of the onomastic
element which strongly suggests, all the same, the relationship of
Bertha with the Merovingians. Besides the names even of Bertha and of
Caribert, her son, it is necessary, in fact, to add the name of Thierry,
borne by a grandson of Bertha, and those of Louis (= Clovis) and Lothar
(= Clotaire), borne by two sons of Charlemagne. It has indeed been
claimed, most recently by J. JARNUT, that in the latter case, only
political motives guided the choice of these names, but that's opposed
to all the onomastic habits of the Franks, according to which only a
direct blood tie could authorize the re-use of a name. S. de VAJAY thus
suggested in 1975 that Bertha of Prum was the daughter of Thierry III,
thus sister of Clovis III and Clotaire IV. This is indeed the better
solution on the onomastic level, but it doesn't seem, on the other hand,
to take stock of the elements imposed by the inheritances. That is to
forget that, as M. CHAUME noted, the spouse of Thierry III was Dode,
probably sister of Pepin of Heristal. Thus, Bertha of Prum, daughter of
Thierry III, would find herself at the same time the cousin german of
Charles Martel, which indeed explains, if she held her parts of
Rommersheim and Rheinbach from her maternal ancestors, the consanguinity
-- in a licit degree this time -- between her granddaughter Bertha of
Laon and the latter's spouse, Pepin the Short, son of Charles Martel: