It was the French under General Leclerc who were the first into Paris.
Perhaps the most stage-managed part of the war. De Gaulle insisted on it, and Le Clerc (real name Philippe, vicomte de Hauteclocque, and the grandfather of a friend of ours) led the French troops past the Americans. They were commanded by Gen. Omar N. Bradley who had stopped to allow them their grand finale. The Americans said that they "honored the French divsion by letting them enter first", but the truth is that it was a direct order from a very high place.
As usual, politics got in the way of soldiering.
Le Clerc died in a plane crash in 1947, and became a French military hero (almost unique), hence there are Avenue etc General Le Clerc in almost every French town and city.