The question is: what if your concentration spell was already in place?
Relevant quote for when you lose concentration:
"Casting another spell that requires concentration. You lose concentration on a spell if you cast another spell that requires concentration. You can’t concentrate on two spells at once."
So while it states that you lose concentration if you cast another spell, invoking the favoured foe ability is not casting a spell. It doesn´t even require an action to be used. My reading is that you can invoke it safely, but it won´t have an effect because you need to chose on which spell/ability you concentrate on.