Oh, I think they'd have given it a go, not least because I know how weak the defences were and that they had several ships designed for attacking forts. Boston's entire fortification system has one condemned gun in early 1862!They responded to the need to establish the blockade, and they would have responded to the need to re-establish the blockade. It would have been costly, but the major ship building yards were capable of building a better navy. I don't the French would have dared to attack Portsmouth, ME, Boston, Brooklyn or Philadelphia.
But even assuming the French don't do that, building a new navy from scratch capable of fighting battleships is going to take more like years than months - which is more than enough time for the French to have landed an army corps.
If France blockades all the US Ports then by definition no one gets cotton.
Er... no? What?
If Charleston and Mobile and New Orleans are unblockaded then export of cotton resumes from the CSA.
If it becomes a guerilla war, they might have trouble, but if it becomes a guerilla war then the CSA is already independent anyway.France didn't do all that well against Mexico don't see why the US any easier a nation to go to East with.