No, Gibraltar citizens are not automatically French citizens. Gibraltar is a British Overseas Territory located on the southern coast of Spain. Therefore, the citizens of Gibraltar are British citizens, as Gibraltar is under the sovereignty of the United Kingdom.

French citizenship is obtained through birth, descent, marriage, or naturalization according to the French nationality law. Being a citizen of Gibraltar does not grant automatic French citizenship.

However, it's important to note that Gibraltar is geographically close to Spain and has a border with it. Therefore, some Gibraltarians may have Spanish ancestry or connections, which could potentially make them eligible for Spanish citizenship.

For example, under Spanish law, individuals born in Gibraltar before 10 July 2010 to a Spanish mother or father may be eligible for Spanish citizenship. Additionally, individuals who can prove their Spanish descent or have resided in Spain for a certain period of time may also be eligible to apply for Spanish citizenship.

References:

1. Gibraltar Government - Department of Citizenship and Residency
2. Service-Public.fr - French Nationality Law
3. Spanish Consulate in Gibraltar - Nationality