Possibly it is however canonically legitimate, in which case it is the most senior extant male-line branch of the Capetians, and senior to the current royal Bourbons.
Its head possesses the title count of Busset since the marriage of the first Bourbon with the baroness of Busset in late 15th century.
The line of Bourbon-Busset descends in the male line from the son of Louis of Bourbon, Prince-Bishop of Liège (1438-1482), himself a son of Charles I, Duke of Bourbon. Louis, in male line a sixth cousin of king Charles VII of France, married, without royal licence, Catharine of Egmont, daughter of Arnold, Duke of Gelderland. Either from this marriage, or from a mistress of Louis of Bourbon, a son was born, who then married the heiress of the barony of Busset and was elevated to the title of count of Busset.
Although the marriage between Louis and Catherine took place before Louis was consecrated as a priest, which would have made it canonically impossible for him to marry, it was kept secret, being against the interests of Louis XI of France. French alliances in the Low Countries were not compatible with those of the House of Egmont. The French king therefore (debatably) annulled the marriage, declaring any children of the marriage illegitimate.
Records and chronicles are unclear as to whether Louis and Catherine produced any surviving descent in the male line. Evidence just as easily suggests that the Bourbon-Bussets derived from an entirely uncanonical affair between Louis of Bourbon and a mistress.
When the Valois-Angouleme branch on the throne was nearing its end in 16th century, Antoine de Bourbon, Duke of Vendôme was recognized as the Premier Prince du Sang, the first prince of blood royal of France, although he only descended from James I, Count of La Marche (1315–1362), the younger brother of duke Peter I of Bourbon.
Were the Bourbon-Busset legitimate, the position of the premier prince would have belonged to the then count of Busset instead of Duke Antony. However, what is certain is that the Bourbon-Bussets, believing themselves to be an illegitimate line, either in law or fact, never claimed the position, and played no particular role in the subsequent events, which resulted almost in a civil war in France between Protestants and Catholics.
Similarly, upon the death of Henry III of France, were the Bourbon-Busset a legitimate dynastical line, the crown should have passed to Cesar of Bourbon-Busset (1565–1630), in male line the late king's 10th cousin. However, he never claimed the crown, and played no particular role when king Henry III of Navarre, his agnatic 7th cousin once removed, Antony's son, became king Henry IV of France and Cesar's liege lord.
The senior male-line descendant of the Bourbon-Busset recently was the French writer Jacques de Bourbon-Busset (1912–2001), member of the French Academy. President Charles de Gaulle was once quoted telling him: Had it not been for the decision of king Louis XI, you might well be head of state of France today, instead of me.
Madeline of Bourbon-Busset (1898-1984), daughter of the then reigning count of Lignières and Jacques's distant cousin, married in 1927 a royal Bourbon relative, Xavier of Bourbon-Parma, duke of Parma and Carlist pretender to the throne of Spain.
They were the parents of Carlos Hugo of Bourbon-Parma, duke of Parma. As wife of Xavier, Madeline was proclaimed Queen consort of Spain by the remaining Carlists in 1952. In 1974, she became titular duchess of Parma in her own right.
Madeline, widowed in 1977, was a staunch adherent of Carlist reactionary ideals, conservatism and clericalism included. Her younger son Sixtus Henry of Bourbon-Parma, duke of Aranjuez continues currently as Carlist pretender.