You have a pretty broad question here. The French pretty much influenced every part of the culinary world prior the boon of nevouex cuisine in the late 70's early 80's--where a lot of the younger aspiring chefs in the states thought it faster and easier to skip the discipline of Escofier's classic french cooking techniques and introduce smaller portion, crispy fusion, trendy, awkward dishes with rampandt inovation. Some would debate this but it is my opinion nonetheless.
This didn't set well with traditionalists. Things changed. I think that the French, by means of thier history and influence, set the standards for cooking technique, the methods and descriptions used in recipes and procedures, have had a huge impact on how our menus describe dishes today. But French menus are different as is French service compared to American. American cuisine is nothing more than an adaption of many influences, mainly French and Chinese.