Stanton's "WW II Order of Battle" identifies the 4th Infantry Division as assaulting Utah Beach, France, 6-6-44, D-Day, along with the 359th Infantry Regiment (90th ID). It was assigned to VII Corps during this time, and was under the command of Major General Raymond O. Barton (from July 42).
Among other elements, the Military Police Platoon is included in the organizational chart. There would be no reason to think that this unit did not participate in the invasion.
The MPs had an important role in the movement of troops having cleared the beach, and later for traffic control as they moved further inland. Prisoner control would have been an important function too.
I note in another reference, that the 4th ID began an advance toward Cherbourg, France, 8 June 44.
Efforts by the 22nd Infantry Regiment (4th ID) to cross the line of German fortifications, which extended from Azeville to Crisbecq, were unsuccessful.
By 9 June 44, the 4th ID had made what was termed "significant progress" in its advance on Cherbourg.
On 20 June 44, the 4th ID was five miles from Cherbourg. The outer defences of the city were entered by elements of VII Corps (4th ID included) on 23 June 44, to mixed resistance. The city was taken 1 July 44.
So, I would assume that Francis was wounded sometime between 8 June and 1 July 44, on the approach to Cherbourg, (or maybe after the city operation ?)
German Elements involved in D-Day:
Overall, Seventh Army, Dellmann, commanding. LXXXIV Corp, at St. Lo. 914th Infantry Regiment, at Breevands 6th Parachute Regiment, at St. Come Dilmont 919th Infantry Regiment, at Ravenoville 709th Infantry Division, at Qinneville 1058th Infantry Regiment, in reserve 91st Infantry Division, in reserve.
There were probably others too, but not indicated on my maps.
And that is about all I can render on the subject of the 4th Infantry Division. I hope this helps in your quest for "more light".
With best regards,
Louie Franklin Turner
For more insight, I recommend:
1. WW II Order of Battle, Shelby L. Stanton 2. 2194 Days of War,Salmaggi and Pallavisini 3. Citizen Soldiers, Stephen E. Ambrose