I am married under the community of property regime (community of acquisitions). I own a real estate property received as a gift, which I rent out. In the event of divorce, can I claim full ownership of the rental income?

No. Pursuant to Article 1401 of the French Civil Code, the fruits (rental income) of separate property constitute community property. Therefore, in the event of divorce, the rental income belonging to the community will be divided equally between the spouses (Article 1475 of the Civil Code).