They are not part of Schengen (but EU citizens don't need any visa, it's mostly intended to curb illegal immigration from South America via Guiana) and have the ability to use different VAT rates from mainland France, but that's all.
The state of British citizenship is a bit more complicated though I think. A bit like US citizenship which kinda depends on which US territory one lives, as far as I understand.
This is what I meant when I said these citizenships work in more complicated ways than the French one.
Not quite, at least not by default. The pre-Brexit Manx passport did confusingly include the text "European Union" on its cover, but holders of Manx nationality were only citizens of the EU if they had lived for at least 5 consecutive years in the UK or if they descended from a UK parent or grandparent.
Source: https://en.wikipedia.org/wiki/Isle_of_Man-variant_British_pa...
> The European Union (EU) has nine 'outermost regions' (ORs): Guadeloupe, French Guiana, Martinique, Mayotte, Réunion and Saint Martin (France), the Canary Islands (Spain) and the Azores and Madeira (Portugal). The ORs are an integral part of the EU and must apply its laws and obligations.