Classical French historiography [fr] usually regards Clovis I (r. 509–511) as the first king of France, however historians today consider that such a kingdom didn't begin until the establishment of West Francia in 843.
Clovis I established a single kingdom uniting the core Frankish territories, and was crowned King of the Franks in 496.
The latter became the Holy Roman Empire, and West Francia eventually became the core of the Kingdom of France, which was structured as a feudal monarchy and lasted for eight centuries (987–1792).
This lasted a year, before the monarchy was abolished entirely in September 1792 and replaced by the First French Republic, marking the beginning of republicanism in France.
From that point on, it was republics down to the present day, with the exception of the authoritarian Vichy regime during World War II.