So in Searocksandtrees's post the British monarchs are discussed. I'll give some info on French Kings.
If you go back all the way to the Merovingian dynasty there has been several Clovis, several Clothaire, ...Etc they were not known by numbers in chronics of the time but by their period of rules, sometimes with a deed they may have done.
However during their lifetime, they were not called by a number until the XIIth Century. But even at this time, they used it that way : Louis the Ninth or Louis the Eight ( in French it would be Louis le Neuvième for example ). The first monarch to have a chronic written during his lifetime and using or know numerotation was Charles the Wise where he is mentioned under the name : Charles V. This remained very rare.
Louis XIV was however called several times as such and not Louis the Fourteenth. Even under his predecessor, writers barely used Louis the Thirteenth but used Louis the Just.
However, most of the people ( I mean low class people or simply people living at the time ) would never use a numerotation to refer to the King. For example you would not say Louis XVI if you lived in 1785 but simply King Louis or Our King Louis. It's only in the XIXth Century that historians started to put a number after all the monarchs even those during the Merovingian dynasty who never saw a number used during their lives. It was certainly done to ease everything.
As to why they are so many monarchs with the same name is pretty much like in England and many other nations. In France, the names were given in function of your godfather and godmother ( both in royal and noble families but also among the people, I saw that quite often during my genealogy researches ) :
For example, Louis XV had more than a dozen of godsons and goddaughters, resulting in plenty of Louis and Louise. The godmother would often give the second name. This tradition also introduced some " new " names. For example, the future Louis XVIII was born Louis Stanislas Xavier de France ( Stanislas being the deposed King of Poland, his grandfather ). Then they took their ruling names.
Why so many Louis ? Well Louis derives from the name Clovis and Clovis was the " first King of France ". That was quite prestigious but then we had Louis the Pious ( Louis Ier ) who himself was remembered as a good monarch and it started to become popular. However, Louis IX, several years after his death became a Saint of the Church. That explains why it became such a popular name among French monarchs. You were named after a Saint who also happens to be an ancestor.
In France we also had ten Charles. Some were quite catastrophic monarchs such as Charles VI or Charles IX but the first Charles was Charles the Great ( or Carolus Magnus/Charlemagne ), a glorious ancestor.
We also had four Henri. The last two, Henri III and Henri IV were murdered and it may have thrown a cold on the name.
So indeed, like in Britain and a lot of other nations, monarchs were given the names of a glorious ancestor or someone responsible for great deeds.
Sources : Louis I, II, III… XIV…L’étonnante histoire de la numérotation des rois de France Michel-André Lévy
hi! there's lots of room for more on this, but you can get started on comments in this post