The American forces on D-Day consisted of the 1st, 4th, and 29th Infantry Divisions, the 82nd and 101st Airborne Divisions, and a lone RCT of the 90th Infantry Division. Each division, save the airborne ones and the 90th's RCT, had an independent tank battalion supporting it.

British forces included the 3rd and 50th Infantry Divisions, and the 6th Airborne Division. The Canadians had their 3rd Infantry Division. Each division, in a similar fashion to the Americans, had an Armoured Brigade in support.

5 divisions were American, 3 were British, and one Canadian. 130-150,000 troops were landed on D-Day, so about half the assault troops were American.

It was the British and Canadians who provided most of the ships to get the troops across the Channel, a large portion of the naval covering force, (four of seven battleships, all seventeen light cruisers, 85 of 135 destroyers, and 352 of 508 other ships) and a majority of the landing craft that moved the troops ashore. The British by far took the heaviest landing craft losses; I allude to this in an earlier question, as well as provide a list of ships that moved the Americans across the Channel;

https://www.reddit.com/r/AskHistorians/comments/3g3f5e/what_happened_to_the_boatmen_who_drove_the/

So as you surmised, D-Day was not a majority American affair, but rather a Commonwealth one.

Sources:

D-Day, June 6, 1944, by Stephen E. Ambrose

Omaha Beach, by Joseph Balkoski