Wikipedia claims:
The He 111Z's operational history was minimal. One such machine was caught by RAF fighter aircraft over France on 14 March 1944. The He 111Z was towing a Gotha Go 242, and was shot down.
and cites :
Nowarra, Heinz J. Heinkel He 111: A Documentary History. London: Jane's Publishing. 1980. ISBN 0-7106-0046-1.
What would a He 111Z be doing towing a Gotha 242 over France in March 1944?
The short answer: exactly what it was designed to do. The He 111z was specially built as a glider tow-plane, able to tow even the biggest military gliders in use by the Nazis. The Gotha 242 was a Nazi military glider, and as such, it makes sense that it might be found beind the He 111z. As to a specific mission in that exact case, who knows? France in March 1944 was still under Nazi control, so it could have been anything from training to repositioning to a commando action - without further details one couldn't say.
The Germans launched a glider attack on the Vercors plateau south of Grenoble after D Day, when the FFI rose against the German occupation. I would, therefore suggest that, as German Glider and other airborne troops were present in France, that this was a training flight.