The more realistic and believable scenario is that France wants the EU Rapid Reaction Force available to be deployed in its far-flung Departments, which are overseas extensions of mainland France. These places are considered, and vote as, part of mainland Departments of France. NATO obviously would not send any troops, ships or planes to sort out any problems in a Department of France, just as it would not send resources to sort out problems in Shropshire or Northern Ireland. But a EU Rapid Reaction Force would of course be sent to those locations if required. British troops would be protecting French colonies, sorry, mainland France. The UK should declare that the Falklands and Gibraltar and other colonies and dependencies are counties of England, Wales, Scotland or Northern Ireland