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Is it possible for an individual to refuse a cheque in France?
In any country, individuals (and shops) can reject any form of payment that is not Legal Tender - defined by law as a payment form that must be accepted. Shops are typically more generous, because they want to do business with you, but individuals are in a different position. In France, only official coins and bills are declared as Legal Tender (so if they don't want to, individuals don't even need to accept bank transfers). This is for doubts you need to pay. In addition, as you are not forced to do business with them, people and shops can require whatever they feel like to require - if you want to buy their car, they can ask you to stand on your head and spit coins, and if you don't like it, they don't sell to you. (They won't do much business then, probably)