Gabriel Aubry just showed up at dependency court in L.A. where a judge will decide if even more restrictions will be placed on his custodial rights.
Sources tell us the judge is expected to lay down a series of orders ... requiring Gabriel to do various things to ensure the safety of 3-year-old Nahla. The judge will hear from the social worker on the case as well as the attorney appointed to protect Nahla's rights.
What's especially significant ... once the judge establishes the ground rules for Gabriel's visitation rights, the case will go back to family court where Halle is trying to convince the judge to allow her to move to France with the child.
TMZ broke the story ... Halle wants to move out of the country because of the problems she's having here with paparazzi and stalkers.