The European Union (EU) started in 1993 and France joined the organization at its formation. However, prior to the EU's formation, France was also a founding member of another major European organization called the ECSC, which is a predecessor to today's EU.

The EU or European Union is not the first organization to unite the countries of Europe. The EU was born from several other organizations, many of which France was a part of. This includes an organization called the ECSC.
In 1952, there was an organization of European countries (similar to the EU today but on a smaller scale) called the European Coal and Steel Community (ECSC),
In 1957, the members of the ECSC signed the Treaties of Rome, which created the European Economic Community (EEC).
This branched off into various communities, including a customs union and a union for the development of nuclear energy.
Eventually, in 1993, the Treaty of Maastricht was signed by 27 European states, thus creating the organization currently known as the European Union. France joined the organization at that time, so 1993 is the year when France joined the EU.