My cousin ... in Paris.

My cousin lives in Paris. (Present Simple).

My cousin lived in Paris last year. (Past Simple).

My cousin will live in Paris. (Future Simple).

My cousin would live in Paris. (Conditional).

My cousin is living in Paris now. (Present Continuous).

My cousin was living in Paris. (Past Continuous).

My cousin has lived in Paris. (Present Perfect).

My cousin had lived in Paris. (Past Perfect).

My cousin is in Paris. (Present Simple).

My cousin was in Paris. (Past Simple).

My cousin will be in Paris. (Future Simple).

My cousin would be in Paris. (Conditional).