It depended. It wasn't unheard of for adolescents and teenagers to go to the guillotine, and mob justice during the Revolution was absolutely indiscriminate - during the September Massacres, it is likely that aristocratic children were murdered alongside their parents (as well as common criminals, Priests, and [men in their 80s] (http://en.wikipedia.org/wiki/Augustin-Joseph_de_Mailly).
The royal children are perhaps the best starting point for this sort of investigation, since they are the most well-documented of all. The Dauphin of France, Louis-Charles, was originally allowed to remain with his parents, his aunt Princesse Élisabeth, and his governess the Marquise de Tourzel alongside his sister Marie-Thérèse Charlotte. The King was first executed, and then Louis-Charles (proclaimed Louis XVII by royalists and his escaped uncle the Comte de Provence) was separated from his mother and aunt and given into the care of the cobbler Antoine Simon.
Reports immediately abounded that the peasant Simon was abusing the young King. This included forcing him to sing La Marseillaise, denounce his family, forcing him to consume large quantitates of wine and there were even reports that the Simons forced the now 8 year old boy to have sex with prostitutes in order to infect him with venereal diseases in order to build a comprehensive case against his mother and aunt (more on that in a second), though this is ultimately disputed. It is known that in the latter half of 1794 the young boy was chronically neglected, despite eventual efforts to improve his quality of life.
Louis-Charles was used as evidence against his mother and his aunt. Libelles surrounding the Queen's Petit Trianon retreat in Versailles had contained allegations of lesbianism and incest, and both were used against the dead King's wife and youngest sister, including a coached testimony from the child himself which stipulated that his own mother had abused him. It was this allegation, famously, which caused Marie-Antoinette to break the silence of her own tribunal and appeal to the mothers in the courtroom.
The 10 year old King would eventually die in 1795, after the execution of his mother, father and aunt. His elder sister, Marie-Thérèse Charlotte, had remained in captivity simultaneously but at The Temple prison. She was released in December 1795 aged 17 back to her mother's family in Austria. Her advanced age had meant that no attempt was made to indoctrinate her into the revolutionary ways as had happened to her brother, and she was largely ignored for her time in captivity. We can only speculate about what may have happened to her if Robespierre had not lost power, though the idea of a marriage to a key revolutionary leader has been speculated about for some time.
The last example I'd like to put forward is not a royal example, but the daughter of the governess of the Royal children of France. Pauline de Tourzel was a few years older than Marie Thérèse but formed a close friendship with both the young Dauphin and the Princess. She, along with her mother and Marie-Antoinette's superintendent the Princesse de Lamballe, was separated from the royal family to Paris' La Force Prison. Pauline was subsequently spirited away in the night by a 'mysterious English gentleman' and was subsequently joined by her mother after the Marquise was acquitted. The Queen's superintendent and confidante was [not so lucky] (http://en.wikipedia.org/wiki/Princesse_de_Lamballe#Death).