Olivier Martinez will not wage a custody war with Halle Berry , sources connected with the couple tell TMZ ... because he does not want to go through with the savagery he witnessed between Halle and Gabriel Aubry .
We're told Olivier was horrified by the bitterness between Halle and Gabriel, and the toll it took on their daughter Nahla .
We're also told Olivier has no intention of moving to France and starting a Kelly Rutherford / Daniel Giersch  type international war .
It's lucky for Halle, because she wanted to move Nahla to France, and tried unsuccessfully to convince a judge it was a better place to raise kids than the U.S.