Are the French capable of landing a strong enough force, complete with a siege train, across the Channel and then be able to maintain that force by means of a secure supply line? The French would only attack the Palmerston forts if a) they needed a good harbour or b) they wanted to destroy the Royal Navy at anchor.
If a) they needed a harbour how did they get there in the first place? If b) under what circumstances would the Royal Navy would be holed up in harbour while the French are in control of the channel?
The forts had their detractors, they were certainly expensive and they would require a large number of reservists to fully man them, but they were a deterrent. One that, presumably, worked. Like the vast majority of fixed works of their era they soon became outdated, but they could still protect the Royal Naval Dockyards from assault.
The French would have to overcome some serious difficulties if they were to be in a position to lay siege to Portsmouth, Plymouth or even Milford Haven. If, and it's a big if, they could, somehow, land a significant force on the south coast they could, possibly, break into the fortress ring at one of the dockyards. I would go for Plymouth, given the choice.
Attack by sea: forts vs ships. Usually a contest that favours the forts. Far easier to aim a gun that isn't on a vessel that is bobbing up and down in, or moving through, water. I guess that the forts, when newly built, would have the greater advantage. Possibly once turreted warships are the norm, and the forts are that much older, the contest might be more even. Still go with the forts though.
Attack by land: forts vs siege artillery. Once again, when the forts are new the defence was probably stronger. Later developments in artillery, especially into the 20th century (possibly a later date than you have in mind) would almost certainly swing things in favour of the attackers. Lots of other considerations though. Do the French have the ability to support a sustained siege of one of the Royal Naval Dockyards. Would they attempt a rapid assault in the hope of catching the defenders either unprepared, or understrength? What is the Royal Navy doing? Would the French target just the dockyards or would they also target civilians? The forts, when built, would have kept an enemy well away from the dockyards although later the ability to fire further would have made built up areas a target. The forts, as built, would have put up a good defence although increases in the power and range of artillery made their resistance less effective as time went on.