For reference, information about the application for the carte de séjour is available at Carte de séjour en tant que membre de famille d'un Européen, but I expect that you are already familiar with this page, for it does not seem to answer this question.
Your experience in Denmark reflects the free movement directive (2004/38/EC), which provides that a family member's derivative rights flow from EU law rather than being subject to the discretion of the host state. Family members with derivative rights therefore typically are able to work from the time they have submitted their application. This is consistent with articles 23 and 25 of the directive:
Irrespective of nationality, the family members of a Union citizen who have the right of residence or the right of permanent residence in a Member State shall be entitled to take up employment or self-employment there.
General provisions concerning residence documents
Possession of a registration certificate as referred to in Article 8, of a document certifying permanent residence, of a certificate attesting submission of an application for a family member residence card, of a residence card or of a permanent residence card, may under no circumstances be made a precondition for the exercise of a right or the completion of an administrative formality, as entitlement to rights may be attested by any other means of proof.
All documents mentioned in paragraph 1 shall be issued free of charge or for a charge not exceeding that imposed on nationals for the issuing of similar documents
After spending more time than I should have searching on https://www.service-public.fr, both from the point of view of a person wanting to work in France and from the point of view of an employer wanting to verify that a prospective employee is authorized to work in France, the best I could come up with was that the receipt for the application might say that it authorizes the applicant to work.
One reason for my difficulty in finding the relevant legal provisions is that the law seems to have changed in 2020, so if someone who has actually done this posts an answer it will be more informative if they have done it since then.