In Ancien Régime France, prince was a rank, not an official title. Legally, only princes of the blood were recognized as princes, but the king could and did unofficially recognize "foreign" princes. This recognition had no legal basis, but was the cause of much controversy at court, since the people recognized as foreign princes often claimed equality or superiority in rank to the dukes and peers. This was further complicated by the fact that many foreign princes were also peers of France.
Some of the more famous houses recognized as foreign princes:
Gonzaga: a princely family of Italian origin.
Lorraine: by virtue of their status as descendants of Charlemagne and as princes of the Holy Roman Empire. (This included the cadet branch of Guise.)
Rohan: because of their status as immediate vassals of and descendants of the dukes of Brittany.
Foreign princes often claimed rights to the style of Highness.