If I recall correctly (it's been a while since I looked at the Convention and the specific implementation verbiage), aircraft carriers are explicitly verboten,

If I recall correctly (it's been a while since I looked at the Convention and the specific implementation verbiage), aircraft carriers are explicitly verboten, but, as you say, non-riparian states also have a tonnage limit on capitol ships which further limits freedom of transit. (Plus some further restrictions on submarines, but those aren't germane here.) In addition, if the US, NATO or France attempted to unilaterally redefine a carrier as a non-carrier capitol ship for purposes of navigation, it would be considered a hostile diplomatic act by Russia, so that also sets limits of its own sort. During the Cold War, of course, it wasn't as important an issue, Turkey being the only NATO Black Sea state (note: since I'm not looking at a map right now, that might not be completely correct). No NATO carrier was going to transit the straits except in a case of war, at which point the Convention would be the least of our problems.