How can I remap these keyboard keystrokes? I am beginning to use the U.S. keyboard because, as a developer, I have the key I use the most available more. 

Only problem is I lost direct access to the accent keys. So I want to remap the keyboard so that Alt+a would give me à, Alt+e would give me è, etc. since I don't use these convenient combinations for anything else.

How can I do this on macOS Sierra?
You can also make accents from the USA keyboard by just holding down the key for the base letter and selecting the one you want from the popup menu that appears.

One pretty easy way to remap keys the way you want is to make a custom keyboard layout with Ukelele:

http://scripts.sil.org/ukelele