At a young age Odin moved to Noumea, New Caledonia, where his father had been transferred, and attended school there.
Upon his return to France, Odin became a lawyer's clerk.
Receiving a bursary, he resumed his studies and qualified as a lawyer.
By 1917, he was an advocate in Bordeaux, and later in Paris.
He ran unsuccessfully as a Radical in the 1919 and 1924 elections to represent Gironde in the Chamber of Deputies, but succeeded in 1928.