The arrests, in the Tarn and Gard areas of southern France, follow last month's decision by a French judge to open a full inquiry into the Spanish attacks.
The identities and nationalities of the three have not been disclosed nor had any charges been made on Tuesday afternoon.
The three are believed to have links with Driss Oukabir, who is currenly in custody in Spain.
He is charged with membership of a terrorist organisation and murder, for his alleged part in last August's Barcelona attack.
Fourteen people were killed when a van was driven into crowds on Las Ramblas boulevard, 100 more were injured.
The following day police shot dead five people in Cambrils, down the coast from Barcelona, after they drove their car at pedestrians and police officers, killing a woman.