French Statute of limitations
Input VAT should be claimed in a VAT return filed no later than the end of the third year following the year during which the deductible VAT was due.
Regarding the obligation to pay VAT, the same general rule applies. The French tax authorities con investigate VAT liabilities up to the end of third year following the year in which VAT became due. There is an extended period of 10 years in case of fraud or "hidden activity".
There is more information available (in French) in the website of the French tax authorities.