The Verdict: Clear Path
You do not need a working holiday visa: as an EU, EEA or Swiss citizen you can live, work and study in France freely. There is nothing to apply for in advance.
If you stay more than three months, you should be working, studying, or have enough resources and health insurance not to be a burden on the French social system.
After five years of lawful residence you acquire permanent residence, and naturalisation becomes possible on the usual terms.