I found this 1998 LA times article that claims this occurred and the film is lost in government archives.

Here are some excerpts:

George Hjorth’s orders that June morning 54 years ago were mysterious: After parachuting into occupied France with his three cameras, he was to hide in front of the German lines at Normandy and film whatever happened on the beach.

It was before dawn on June 6, 1944, and Hjorth was in the dark, literally and figuratively. He had no idea what to expect on that now-fabled stretch of coastline.

Only when the invasion began did he learn that his mission was to film the D-day landing of the U.S Army’s 1st Infantry Division and 29th Infantry Division at Omaha Beach--from the German side.

But whatever he saw, Hjorth (pronounced “Yorth”) was under standing orders not to discuss it for 50 years. Even today, the Cypress retiree’s mission remains an enigma: The film he shot, called unique by historians who recently learned of it from declassified documents, is missing.

“We’re hunting it down,” said Douglas Brinkley, a professor of history and director of the University of New Orleans’ Eisenhower Center. Hjorth’s movie footage and photographs--probably gathering dust in a government archive--are the only known invasion pictures from the German perspective shot at the Normandy beaches, he said.

That article was almost 25 years ago. So, what happened? Is the film lost? Is the story not true?