It depends on the EE. Genetically you don't know if she is pure for the blue egg gene or of she is split with one blue and one white. There is no standard for EE's. It is also possible some of your EE's are pure for the blue egg gene and some are split. You can't tell by looking at the egg if the hen is pure or split.
If she is pure for the blue egg gene and she is laying green eggs, all her offspring will lay green eggs. She already has some brown mixed in and the rooster will contribute a little more. The eggs should not be true blue. But the shade of green could be lighter than the hen is laying now.
If the EE is pure for the blue egg gene and is currently laying blue eggs, that means she does not have any brown to contribute. But the Favorelle rooster should contribute some creamy brown genes. The eggs should not be as blue as the hen is now laying. I'm not sure what shade they will be, but it will probably look more green than blue. That's part of the fun though, you really don't know.
If the EE is not pure for the blue egg gene, which means she has one blue egg gene and one white egg gene, some of her offspring should lay green eggs and some should lay brown eggs. How green or brown depends on the brown eggshell genes contributed by both parents.
None of the eggs should be really truly white,but some could be creamy colored. None should be truly blue but some could be a real light green, maybe pretty close to blue.
You might consider it a problem with the EE, You don't know for sure that she has two copies of the blue eggshell gene or one blue and one white. So you don't know what you will get. For me, that would not be a huge problem, but I would want at least some blue or green eggs.
What I''d expect you to get is pullets that either all lay green eggs, if all your EE hen's are pure. But that shade of green could vary quite a bit since you now have hens that are laying blue eggs and some that are laying green eggs. Or you will get some pullets that lay these different shades of green and some that lay different shades of brown if all your EE's are not pure for that gene.
What I do not expect you to get is eggs that are either olive green or really dark brown since your chickens do not currently lay dark green or dark brown eggs and the Favorelle rooster will not be contributing any dark brown genes. Either way, I think the eggs will look great in the basket. I really like those colored eggs.
I once hatched four pullets from green eggs. Only one of those pullets laid green eggs, The other three lay brown eggs. I then hatched three pullets from the green eggs that the one was laying. None of those pullets lay green eggs. The odds say I should have gotten 3 or 4 green egg laying pullets from hatching 7 pullets from green eggs, but I only got 1. You really don't know what you will get. I got some roosters too but I'm not counting those. They don't lay eggs.