Gap year question.

I don't think that it is stupid at all - after all, if you plan to start working in London, an internship in Paris might be your only opportunity to live in France for a while.

However, bear in mind that you need to speak French fluently (I suppose you do), and that applications in Paris will likely be biased towards HEC/ESCP/ESSEC students. That's unfortunately the way it works, and French banks usually take Master students (due to the system of classes prepa, that I guess you are familiar with).

Then to answer your question on whether it makes sense to go to Paris while you can go to London: I personally don't think that going to Paris for IBD while you can get London IBD, and want to work in London long-term, makes sense (of course this is a personal opinion - I have interned in London IBD and worked with French coverage team, and from what I have seen hours were terrible, and the responsibilities differed significantly from the ones you would get in London). I would rather do a PE internship in France in a fund that is particularly active in the country and that typically takes 6-months interns: think Bridgepoint, Cinven.

A good gap year structure could then be: 6 months in IBD London (off cycle - or less than 6 months), and 6 months in PE in Paris.