It depends on the bequeather. As part of a will, you can designate one or more people who will be responsible for ensuring that your last wishes are carried out. We are talking about an executor.
If the function of testamentary executor is exercised free of charge (article 1033-1 of the Civil Code), the testator is free to provide for a remunerative legacy, commonly called "diamond" for the benefit of this executor. The compensatory bequest must not be excessive in relation to the faculties of the settlor, or the services rendered.
On the other hand, the testamentary executor can obtain the reimbursement of the expenses that he will be able to bear within the framework of his mission and which are the responsibility of the succession (article 1034 civil code).