I know that the person living in Czech Republic in France would be tchèque, but I'm not sure what would be the difference of that word between masculine and feminine.
There is no difference between feminine and masculine form. Only the context, and in particular pronouns used with the noun or adjective, will characterize the gender of the person you're referring to (i.e "Elle est tchèque, il est tchèque", or "Une Tchèque, un Tchèque").
Note that this is not particular to Czechs, it's a rule that applies to most nationalities whose french designation end in "-e" in the masculine form, i.e Russian (un/une Russe), Bulgarian (un/une Bulgare), Slovakian (un/une Slovaque) etc. Swiss being the only exception.