According to Gatun, Panama has done nothing and has no statutory power to act and no statute by which a person born a Citizen of Panama can get rid of his or her citizenship although the Constitutional issue is not citizenship or statutory pattern in the birth country but the sovereignty power of the country where born.
Your son is a naturalized citizen under the statute; I don't know what the French statutes are but at least as to the Constitutional Article II, Sec. 1 eligibility issue, that is not significant. Hopefully, your son does not grow up wanting to be President.
You may very well be right but that is not my understanding.