In 987, Hugh Capet was elected to fill an vacant throne. Nobles didn't care much because thy thought of him as a weak king. But during his rule he made rival nobles fight each other and gained land. Also during his rule he gained the support of the church.
Go seize Boniface
Philip Augustus strengthen the royal government. Instead of having nobles in government position he used paid middle-class. He also introduced a new national tax system. As for warfare he took back English-ruled lands. During his rule he was named the most powerful ruler.
If there's problems I will be the judge
Louis IX was perhaps the most admired French ruler. He ascended to the throne in 1226. He embodied the perfect medieval Monarch. He was also declared a saint within 30 years of his death.
Philip IV during his rule he ruthlessly extended royal power and collected cash from the clergy. Which led to a clash with the Pope Boniface VII. As the problem rises Philip sent troops to seize Boniface. When a Frenchmen was elected as pope. He moved the papal court to Avigon.
Saint Louis was a deeply religious man. He pursued religious goals that were acceptable to Christians. Like Charlemagne he did much to improve royal government and sent out roving officials to check on local officials. He expanded the royal courts, outlawed private wars, and ended serfdom in his land. He even heard cases himself to ensured justice. By the time of his death in 1270, France was an efficient centralized monarchy.
Philip was able to gain support from the French by setting up the Estates General in 1302. This had representatives from all three estates: clergy, nobles, towns people. Although French kings did consulted with the Estates General, it did not have the same power as the English Parliament.