Cousin marriage

If you are Belgian, then you cannot be non-EU.

Ask a notaire/notaris, their advice should be free, but I suspect that, as you are a Belgian citizen, Belgian law will apply and the answer will be no, with Belgium considering you to be unmarried.

According to Wiki, cousin marriage is not illegal here so your problem will be convincing the authorities that the marriage is genuine and not simply a way for your partner to gain access to the EU.
Each case is considered on its merits and there is no general rule which applies to everyone in your situation. Perhaps a better place to ask your question is at your commune.

I think KASSEISTAMPER is right, legally cousins can marry in Belgium, so there is no reason for the marriage not to be recognized. You should note that even married to you, entry to Belgium is not guaranteed, your cousin will still need to apply for a visa.

I don't know here but certai lay in the UK a the closest relative you can wed legally is a cousin.

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