Halle Berry SHUT DOWN in Custody Battle -- Nahla Stays in U.S.A.

Halle Berry just lost big in court -- a judge has ruled she cannot permanently move her 4-year-old daughter to France ... TMZ has learned.

Halle had been fighting tooth and nail with her baby daddy Gabriel Aubry to bring Nahla to Paris, where Halle wants to live with her fiance Olivier Martinez.

Halle argued the L.A. paparazzi scene made life in California too dangerous for her and her daughter -- but today the judge in the case ruled in favor of Gabriel, refusing to let Halle jet to France with their kid.

The full details of the ruling are unclear -- but one thing's for sure ... Halle did NOT get what she wanted.