Hi EllanVannin, welcome to the forum.
Nice first question
I'm not sure I understand you correctly: will you be living in Geneva and work in France? (since you mention you move to Geneva but will commute from France?)
The frontier worker rules can be rather complicated. Therefore, I can only give a general comment. If you live in CH and work in FR and receive official frontier worker status, you will be taxed in CH, since under the frontier workers agreement between CH and FR you will be taxed in the state where you live (i.e. CH). This will include the Swiss federal tax (Bundessteuer).
I would advise you to get professional guidance on this, don't rely on EF knowledge too much...