I think that if the baton makes it way back to Portsmouth in time, it is safe to say that it will make its way to Paris via the ferry somehow.
Convincing somebody to sail the baton across the channel - avoiding thus any form of motorised transport - would propel the whole exercise out of the cool scale.
Assuming the baton is brought to Cowes on the 6th of July, I would manage easily to find a boat who does the Cowes to St Malo race (they are weight concious but 100 g would be OK) and may be able to convince people of the French forum to cycle it from St Malo to Paris!!!
No idea for the return though.
That's a job for Pancho, isn't it?
I could do the Solent -> Cherbourg (ish) leg (weather, work and family permitting). St Malo adds a bit more complexity[1] to the exercise for a simple cruising sailor such as me.
Not sure about bringing it back from Paris either. That's a trek up the Seine which would need me to become a legal sailor in French eyes (paperwork and exams and boring stuff us Brits don't need) and, maybe to remove the mast. You're also looking at a long trip Pompey -> Paris and I don't think Mrs P will let me out unsupervised for that long.
But if a cross-Channel link is needed just ask and I'll see if anything is feasible. I have a folder in a locker if needed.
[1] Two aspects of complexity: more time at sea and therefore requiring someone else on board 'cos I start to see (and, sometimes, talk to) things that aren't there if I stay awake too long. Not good or safe seamanship to be doing that too often. Also, I've not been to St Malo before but my memory of the West coast of the Cherbourg peninsular is that it's all fast tides and sharp rocks.