During the times of the Direct Capetians, the official status of younger Capetian sons was no more exalted than whatever title they were granted. This includes such men as Robert of Burgundy, Hugues of Vermandois, Robert of Dreux, Pierre of Courtenay, Robert of Artois, Alphonse of Poitiers, Charles of Anjou (ancestor of the Capetian House of Anjou), Robert of Clermont (ancestor of the Bourbons), Charles of Valois, and Louis of Évreux. In practice, however, being the sons and brothers of kings gave them unofficial levels of clout and often greater wealth than non-royal counts. Charles of Anjou and Charles of Valois, for example, were able to muster the resources try to claim foreign crowns, though only the former succeeded. Charles of Anjou's descendants, who became kings of Naples and Hungary, enjoyed generally close ties with their French cousins: Charles of Valois married his double second cousin, Marguerite of Naples, Countess of Anjou; Louis X's second wife was Clementia of Hungary; and Louis I of Anjou was designated as heir by Jeanne I of Naples, which subsequent Valois, including Louis II of Anjou, Rene of Anjou, Charles VIII of France, and Louis XII of France, became obsessed with making good on.

However, again, this wasn't officially granted precedence. This is best illustrated when Isabelle of France supposedly protested her son, Edward, giving homage to her cousin, Philippe VI of France, because Edward was the son of a king while Philippe was only the son of a count — nevermind that the count had been her own paternal uncle, Charles of Valois.

The accession of the Valois kings, of which the aforementioned Philippe VI was the first, saw the creation of the title prince du sang, though agnatic descendants they wouldn't been given official ranking over all other members of the peerage until 1576.

How the other cadet branches other than Capetian House of Anjou fared differed: the Vermandois went extinct within three generations and the Courtenays' fortunes were ruined by their adventures in Byzantium, after which half of the family that went east took up residence at the court of Charles of Anjou and married into his family and the few that stayed in France declined into genteel poverty and political irrelevance. In the 17th and 18th centuries, the Courtenays tried to claim the status of princes du sang, but without success. However, the Dreux and Bourbons did very well for themselves, all things considered: the last member of the House of Dreux was Anne of Bretagne, the twice queen of France, and the Bourbons eventually got to become kings of France and later, Spain and the Two Sicilies.

I'll do bastard sons in another comment.