Problem Function mail()

I do not speak English, I use google translation, I’m sorry if the translations are not very correct
I just created a contact form, the user can choose the recipient of the mail. I use the mail () function. Only Gmail receives emails, other addresses nothing. Could you help me to overcome this problem?
Thank you so much.

In french :
Je viens de créer un formulaire de contact, l’internaute peut choisir le destinataire du mail. J’ai utiliser la fonction mail(). Seul Gmail reçoit les emails, les autres adresses rien. Pourriez-vous m’aider afin de palier à ce problème.
Merci beaucoup.

It would be likely a blacklist on our side, you could upgrade to resolve it or use alternative hosting.

That works without issue must be as it uses their script server to send or something?