My spouse refuses to contribute to household expenses on the grounds that my salary is higher than his. Does he have the right?

No. Married couples are required to contribute to the expenses of marriage and the maintenance of children, regardless of their matrimonial regime.
The wedding expenses include various expenses, in particular those relating to accommodation and food.

If the spouses are free to provide in their marriage contract a distribution of the charges between them, they cannot however provide for total exemption of the latter (article 1388 of the Civil Code).

In the absence of an agreement between the spouses, the distribution of the charges is made according to their respective faculties (article 214 of the Civil Code).

If your spouse refuses to fulfill his obligations, he may be forced to do so by the family court judge (JAF). You must file your request directly with the registry of the judicial court of your place of residence or send it by registered letter with acknowledgment of receipt (cerfa n°11525*07).