The Geordie scored both goals in his first appearance for the fallen French giants.
The former Liverpool and Newcastle striker dropped two divisions from L2 Amiens to sign for Bordeaux last week.
Babacar Leye had Voltigeurs 2-0 ahead at halftime before Carroll's intervention.
The former England international first struck a low volley on 72 minutes, then he scored with a trademark header in the 88th minute to rescue a point for his new club.