We are married and have no children. When I die, will my husband inherit my property even though we are married under the separation of property regime?

Yes. When a person dies without descendants, their surviving spouse is entitled to inherit their estate, either alone or in concurrence with the deceased's father and mother (according to articles 756 and 757-1 of the Civil Code). Civil law defines the 'successor' spouse as the surviving, undivorced spouse of the deceased (as stated in article 732 of the Civil Code), with no further reference to the spouses' matrimonial regime. While the matrimonial regime may impact the composition of the spouses' assets, it does not affect the status of the surviving spouse as an heir.