We bring you an excellent article by Susan Abernethy about the Regent of France through most of Richard’s reign. Note the different constitutional arrangements to Richard’s appointment as Lord Protector and Defender of the Realm but France adhered to a Salic Law meaning that neither Anne nor her descendants could ever reign:
For a comparison of the arrangement, try:
Of course, France’s hypothetical monarchy, through the principal claimants, still does adhere to a Salic Law. That may explain why it remains hypothetical.