As Bayart said, you are mistaken. Although de Gaulle's forces claimed that the Vichy regime was illegitimate, it it very difficult to justify the claim based on either popular support (Vichy and Petain almost certainly had the support of the majority of French at the surrender of the Third Republic, and for years afterward) or diplomatic recognition (Vichy had recognition from dozens of countries, including the US and Canada). Conversely, de Gaulle himself had difficulty in justifying his claim that he was legally acting on behalf of the Third Republic.