No! There is an equivalent it's "avoir plusieurs casquettes" i often hear that in my work ;-) litterally it's " I have many hats". Of course every other expressions that Cherry told are also good. But i think that "avoir plusieurs casquettes" is the closer one.

No there is no equivalent idiomatic expression using 'hat ' ,you would rather say ( maybe there are other idioms French people know about ) exercer plusieurs fonctions assumer de nombreux rôles occuper plusieurs postes .

In fact it's the same: we say "j'ai plusieurs casquettes".