As we all know, Fermat has stated his theorem at the corner of a book. That is far from the standard way of representing a theorem. He said he had a proof which we never saw. So before it was proven true by Andrew Wiles was it assumed that Fermat actually had a proof and thus its a THEOREM or it was called a CONJECTURE till it was proved by Andrew Wiles.
Mathematicians speculate that Fermat may have made a subtle error in a proposed "proof" such as for example the error of assuming unique factorisation of algebraic integers which was the basis for a 19th century incorrect proof apparently by Lamé.
It is considered unlikely that Fermat had a correct proof. The odds are against it, given the number of people who have worked on the problem and continue to do so :-)