Catherine de Medici's uncle was pope, and then she was a good match for french royal family.

But she married the second son of François I, and consequently, should not have become queen.

But the death of Dauphin François de France led her to become Queen, cause her husband was the new heir to the throne.

When her husband, king Henri II died, she led the Regency.

She was the mother of three different kings (françois II; Charles IX; Henri III). This is the record in french history.

u/Jean_sans_Peur is right.

Catherine's parents died when she was very young, making her a very very rich young lady and more importantly a potential future bride for many Catholic princes in Europe who were looking for money and a close link to the papacy since her uncle ( Leo X ) and later her cousin Clemens VII were Popes.

At that time and since many decades, France was hugely interested in Italy ( the Italian Wars ) and Francis I ( François ) was looking to take the lands of Milan and Genoa. Marrying one of his sons to the a close relative of the Pope ( and a rich one ) would ensure an alliance and the support of the papacy and perhaps the papal armies. The dowry was very important, especially for a France that was in need of money.

However, the plan did not worked that well in several ways. The death of Clemens VII and the election of a new pope, unwilling to keep the agreement and the alliance with France prevented Francis I from receiving the dowry and the papal support. Later, the death of Henri's brother, the Dauphin François, pushed the young couple of the throne of France, when Francis I passed away.

Source : Les Rois de France by Jean-Baptiste Santamaria

Decent answers here, I'd just like to add one or two bits of information for clarification: that there was grumbling at the time that Catherine was a "shopkeeper's daughter", but at this point in time, the Medici had managed to dismantle the apparatus of the Florentine Republiuc and rule as Grand Dukes of Tuscany. Catherine was, for all intents and purposes, a member of the ruling family of a very wealthy sovereign state, and could hardly be defined a woman of Low Birth.