Following his unsuccessful wooing of queen dowager Isabelle de Valois, Henry of Monmouth, prince of Wales was the subject of several betrothals. The brides offered were:
1) Marie de Valois (sister of Isabelle and Catherine), who when the envoys approached her to convince her to exchange a heavenly for an earthly bridegroom, laughed at the idea.
2) Catherine de Valois
3) Katherina of Denmark
4) an unspecified daughter of the duc de Bourgogne
5) Marie de Bretagne (married to the duc d'Alençon to prevent English intervention in Bretagne)
6) An Aragonese infanta (either the OTL queen of Castile or Portugal)
Another betrothal (though offered to the widowed duke of Lancaster, rather than his son) was one of Carlos III of Navarre's daughters (Maria, Beatriz or Isabel), nieces of Hal's stepmother.
So who should be princess of Wales/queen of England? And what might the result be of Henry leaving a non-diaper-dirtying rugrat to succeed him when he dies?