In the Kingdom of France, the Salic Law limited the succession to the throne to the patrilineal descendants of kings. As such, they are in the line of succession to the French throne, and were called "Princes of the (royal) blood."
The principle of male-line succession arose in the early 14th century out of the peculiar circumstances that led to the extinction of the direct line of the House of Capet. Such right was contested by the English House of Plantagenet, but the Valois eventually secured their right by their final victory in the Hundred Years' War. It is notable that the English royalty maintained their nominal claim to the throne of France, and maintained the French fleur-de-lys in their arms. The French kings deigned not to force them to surrender such nominal claim.
The House of Bourbon Edit
Valois victory did not merely secure their own right to the throne, but also those of the other branches of the Capetian dynasty, such as the Bourbons.
By the end of the first half of the 16th century, the collateral lines of the House of Valois had become extinct. This increased the importance of the already powerful House of Bourbon, who are next in the line of succession.
But while the last Duke of Bourbon chose to fight in the service of the Emperor against the King of France, the House of Bourbon-Vendome (to which Antoine and Louis belonged) remained in the service of the King of France. Much of the Bourbon wealth were confiscated when the Duke of Bourbon left France. The Vendome branch, in the person of Antoine, managed to acquire a royal title. It would take another generation before the French throne itself was inherited by Antoine's son, Henry. The French religious wars would end only near the end of the 16th century.
In Reign Edit
In Reign, the succession right of the Bourbons was considered a threat to the Valois. Francis deemed it wise to force Antoine to renounce his right to the throne.
In historical reality, the French strongly respected the order of primogeniture, especially with respect to the throne. For this reason, Antoine could not legally claim the throne while Francis and his brothers lived; neither could Antoine legally renounce his right to the throne, for that would disturb the order of primogeniture. The status of prince of the blood, and the succession rights on which it was based, can be acquired only through birth and lost only through death.