Huh?!?? Jira, from Atlassian, is a Issue and Project Tracking application. It is not a Test Management tool.
I have been using Jira, on and off, for years. I thought that maybe it has changed and now supports test management. Or maybe Atlassian has a Test Management tool which integrates with Jira. So I went to the Atlassian website. When I look at the Jira page there is nothing about it being Test Management software. There are plugins for integrating other Test Management software with Jira but even those seem to be for gathering metrics on testing and not necessarily launching and and recording Selenium tests.
Personally, I have obtained a JUnit plugin for Confluence (not Jira). It was in their Advanced Macro package. {junitreport} could be added to a Confluence page. It would display the JUnit test results for JUnit XML files dropped in the specified directory. I would write my test framework to use JUnit and copy the results to a directory which Confluence could then monitor. After each test run the Confluence page would update to show the current and all previous test results. I then made sure the test suites and method names made it easy to track which tests related to which requirements/testcases.
BillR's recommendation of TestNG or JUnit would work well for generating test result XML files. Something like cucumber would be a BDD (Behaviour Driven Development) test tool. I'm not so sure it would integrate with Atlassian tools. I have never used BDD tools with things like Jira or Confluence.
If you a stuck on integrating Jira with something I would recommend going to the Atlassian website and searching the marketplace for plugins.
Darrell