I booked a plane ticket to Argentina with my name as it is on my Tunisian passport. Recently I changed my first name on my french passport so the first name doesn't match the one for the plane ticket/Tunisian passport. So my question is can I travel to Argentina using my Tunisian passport as document of identification and my french passport as a visa/proof of right of entry ? Or the airline may refuse it. Is there any other solution than applying for Argentinian visa with my Tunisian passport ?
You won't have any problems. Use your Tunisian Passport to buy the ticket and make the check-in. On arrival immigration you should show your French passport.
Same process when you leave.
Check-In with Tunisian passport, and exit immigration with French Passport.