In his decision, obtained by TMZ, the judge chose to make Kelly's ex Daniel Giersch the "residential parent" because "Daniel (who lives in France) has facilitated the relationship of the children with Kelly ... and Kelly simply has not done so."

One glaring example -- the judge says Kelly continually failed to put Daniel's name on their daughter's birth certificate ... despite being asked several times by the court.

The judge writes, "Even while under the scrutiny of an extended trial, Kelly still has declined to demonstrate the level of commitment to facilitating the relationship that would be required of a residential parent in a relocation situation."

As we reported, Kelly gets the kids (aged 5 and 3) 50% of the time under the new arrangement, but the children will live and go to school in France. Daniel can't return to the U.S. because his visa has been revoked, so Kelly will be spending a lot of time on a plane.

As for the details of the new custody plan -- Daniel has to buy Kelly six round-trip airline tickets to France per school year (coach class) ... and put her up in a house with a car while she's in the country.