I haven't used Jenkins or its integration with Rally, so I can't speak to that, however Rally does have a Release Summary and a Release Traceabilty app. Essentially they give you a list of all the stories and defects scheduled in a release (the traceability one also has tasks and test cases).
Release Summary:
https://github.com/RallyApps/ReleaseSummary
Release Traceability:
https://github.com/RallyApps/ReleaseTraceability
If those don't work outright for you, they might be a good starting place (though the version of the API they use are depreciated).
If the name of the User Story does not help for the release notes, you could always add a custom field to stories for a more release note friendly description, and then query against that field for all the items in a given release to produce a report.