Let $(T_1,g_1)$ and $(T_2,g_2)$ be two flat tori of dimension 2 such that their geodesic flows are $C^0$-conjugated, is there an isometry between $(T_1,g_1)$ and $(T_2,g_2)$ ?

I emphasize the fact that I ask a $C^0$-conjugacy. In the paper of Croke mentioned below in the answer it is a $C^1$-conjugacy.