As long as you enter FIDE rated tournaments you should be OK. If the arbiter is a FIDE International Arbiter he is required to know English. English is the main FIDE language and according to FIDE Regulations for the Titles of Arbiters -
4. Requirements for the title of International Arbiter.
All of the following:
4.3 Obligatory knowledge of English language, minimum at conversation level; and of chess terms in other official FIDE
Arbiters with just the FA title are not obliged to have good knowledge of English but will need it if they have ambitions to become IAs.
That said, the French are notoriously bad at foreign languages. I went to live and work there after having lived and worked in Germany for some time and the contrast was stark.
My experience going to open a bank account in Munich went something like this -
Me to stereotypical gorgeous, blonde teller: "Entschuldigung Sie. Ich moechte ein Konto oeffnen"
Brunhilde: "Certainly sir. Your passport please? You are working at Digital?"
I tried the same thing only in French at the bank near where I worked on the southern edge of Paris and got a reply in French. With my schoolboy French it was a struggle but she was patient and I just about managed.
For chess tournaments you might be OK but for general life I would strongly recommend you have French lessons while you are there.
Also, if you are the Owen Rees with FIN 343113860 then I would recommend you try and get a proper FIDE ID number before you go. If you are in England (might also work in Wales) then the cheapest / easiest way is to enter a FIDE rated blitz tournament. The ECF doesn't grade blitz and FIDE don't charge federations for rating blitz so you will end up getting a FIN free of federation membership fees.
PS. I'm guessing you already know "j'adoube". The other useful word is "remis" for when you want to offer a draw.