I hope it is not too late to answer the OP question (don't come that often).
I have an qwerty english keyboard and my regional and Language Option is set to English (United States), so I am probably on the same setup that you.
- To get the è character: [Ctrl]+[`] (up left on the keyboard, left of the 1), then hit the e key.
- To get the é character: [Ctrl]+['] (middle right on the keyboard, right of the

, then hit the e key.
- To get the ê character: [Shift]+[Ctrl]+[^] (top part of the 6 key), then hit the e key.
Same thing with other characters: à, ù, û, î, etc...
This is the easiest combinations I found to do them.
Be aware that some softwares(like this forum) won't accept the combinations and you will have to create them on another software (Word for example) and then copy-paste them.
Hope this helps.