Surely you are not the first person with this conundrum. Doesn't the school
offer any other payment options? I mean, everyone coming to a language
school is (more or less) by definition coming from a different country and
won't have a French bank account.
I've used Wise, which is one of multiple international Venmo/Paypal type
payment systems, to pay small business owners in France who don't want
the overhead of credit cards. The recipient gets Euros deposited into their
account with no fees, and you pay minimal fees compared to using a major
bank.
I suppose the other alternative is to get the Euros from your US bank before
you leave, but there may be a non-trivial cost to that, and then you're carrying
them a much longer distance/time.