After my mother’s death, my father and I invested the inheritance money in a capitalisation contract, under which he holds the usufruct and I hold the bare ownership. Can he redeem the contract without asking for my consent?

Yes, but… In a dismembered capitalisation contract, the usufructuary has the right to manage the contract and to make redemptions (partial or total) without the bare owner’s consent (Article 578 of the French Civil Code), unless otherwise stipulated. However, upon termination of the usufruct, the usufructuary must return to the bare owner the redeemed value or assets of equivalent value.