My husband and I have been living apart for several years and no longer have any contact. I found out that he's started a new life. Is it possible to deprive him of all the rights to my estate?

No. Subject to the absence of children and the predecease of the deceased's father and mother, the surviving (non-divorced) spouse is entitled to the full inheritance of his or her spouse (art. 757-2 C. civ.). 
Although you can reduce your husband's rights by bequeathing your assets to whomever you wish, these donations cannot exceed 3/4 of your estate. Given your family situation, your spouse will benefit from a hereditary reserve of a quarter of the inheritance assets (art. 914-1 C. civ.).