It was a stipulation of the Second Armistice at Compiègne between the Vichy French government and the German Reich that all French POWs would remain imprisoned as POWs until the cessation of hostilities against the Allies, i.e. the defeat or capitulation of Britain. This stipulation extended to all Allied personnel and therefore Vichy French authorities would have been bound by law to hand over re-captured POWs to the German authorities.

The extent to which this was enforced was likely a matter of local sentiment.

While it's true that there was some public support for the Vichy government early in its life that quickly dwindled as the harsh tributes and similar stipulations of the Armistice bit down and then vanished altogether when the Germans occupied the southern "Zone Libre" in response to the Allied invasion of North Africa in 1942.

Certainly by the D-Day landings public support had turned essentially 100% against what was by then recognized as a purely puppet regime and the stories of assistance from French resistance fighters to allied POWs or downed pilots are well known. However the "law" remained that POWs were to be turned over to German authorities until the Free French government lead by Charles De Gaulle reclaimed the territory.