Upvote:9
No, this won't help at all.
The ESTA application process requires you to disclose other passports that you have so, if your friend filled out her previous ESTA forms correctly, she has already linked her French and Norwegian passports to her identity. She will also have to make a new ESTA application for her Norwegian passport which, again, requires her to disclose details of her French passport. If she lies then, on arrival, she'll be linked to her French passport anyway by her fingerprints and photograph and will very likely be refused entry for deception.
She needs to deal with whatever it is that's causing the hassle. For example, if they think she can't support her trip, she should bring bank statements to prove she has enough money. If they think she might not go back to France, she needs to provide evidence of her commitments there (employment contract, ownership of significant property such as a house or car, etc.)