France treats its overseas territories differently to the UK. Whilst Britain allows its overseas territories a good deal of autonomy to run their own affairs, maintaining overall control and acting as final adjudicator in all decisions, France treats its overseas territories almost as integral parts of France. Just not connected to the French homeland. Each territory also has representation within the French government.
The overseas territories are legally either a Department, which treats it as a direct part of France, essentially using the full French legal and governmental system to govern the territory, with only limited rules being allowed to be adapted to suit the local situation. A Collectivity does not enjoy as much representation in the French governmental system, as they are allowed greater autonomy in making their own rules and laws, with limitations. For example, foreign policy and defence is left in the hands of the government in Paris.
Many of the territories formally use France's Tricolore, however, if a territory also flies a unique flag of its own, I will list the territory below!