I know Germans used captured Soviet tanks, one example was just rescued from a bog in eastern Europe, but I have never seen or heard of the Western Allies encountering T-34's or other Soviet tanks when fighting in France or Italy. Where the tanks transferred to other units when the original user was pulled off the line, or were no units that had captured tanks ever transferred away from the eastern front?
Well, there are some instances of Russian equipment being found in Normandy, most likely at a training ground or perhaps abandoned by a police battalion, but there is no evidence I am aware of that says that the Western Allies fought against Soviet equipment in NWE.
Here are some pictures of the equipment found:
Various captured tanks including a T-26, T-34, M13/40, and numerous French tanks.
I am sorry I couldn't be more helpful. :/