This title seems to be associated with liberals in this period and a less controlling monarch.

You are right. The Kings of France ( from Philippe Augustus to Louis XVI, before they were Kings of the Franks ) were kings by divine grace. Their role as kings was granted by God which is what gives them the right to rule.

However, after the 1789 Revolution and the establishment of a Constitutional Monarchy with Louis XVI as monarch, then the July Revolution in 1830 when the deputies proclaimed Louis-Philippe d'Orléans as king, the title was changed to King of the French. This symbolized the transition of kingship being given by God to being given by the will of people. King of French is a title showing that the sovereignty of the monarch is granted to him by the people and no longer by God. It makes the king dependant on the people, he has to answer to it for his actions. This is the transition where the king only has to answer to God to a Constitutional Monarchy.