The company said flight AF111 was forced to land in Hamburg, Germany, early Wednesday to refuel because the plane had too little fuel on board to complete the flight following its detour.
Hamburg Airport confirmed that the plane landed shortly after 6 a.m. (0500 GMT) and was able to take off for Paris again after an hour and a half.
It wasn't immediately clear if Russia's military exercise was linked to the increased troop activity on its western border with Ukraine.
Meanwhile, the World Bank warned Wednesday that Russia's economy could contract this year if the country is hit with more serious sanctions following its annexation of Crimea.
