Ahh........good question. To make a long story shorter, I can't find a photo of one in Normandy after looking through about 15 books on Normandy, Marder III's and Panzerjagers. Model M's, no problem. Two of my books both state that model H's served in Russia, Tunis and Italy, no mention of Normandy.
Production of H's ended in April of '43, so it's a little late to find them in Normandy in '44. These weren't exactly the most robust of vehicles ever built, and a year of service on the Eastern Front would not have been kind to them. But there were much older vehicles found kicking around in Normandy, even such clunkers as WW I FT-17s. Since more than 3 times as many ausf Ms were produced and production didn't end until May of '44, these are easy to find in Normandy. Sorry, but I pass on this one.