Possible Original Research:
I only skimmed through on these parts, but it seems to me that most of this needs to be cited - either for verification, or simply for the sake of further reading.

1. French people often refer to Metropolitan France as L'Hexagone (The "Hexagon") because of the geometric shape of its territory.

Unless it was a Frenchman or Frenchwoman who added that in, how can we know for certain that they really do? Is this self-made nickname for that region so internationally renowned that it's a surefire fact? Unless one can respond in the affirmative to either question, It needs a citation.

2. There are various theories as to the origin of the name of the Franks. One is that it is derived from the Proto-Germanic word frankon which translates as javelin or lance as the throwing axe of the Franks was known as a francisca.

Another proposed etymology is that in an ancient Germanic language, Frank means free as opposed to slave. This word still exists in French as franc, it is also used as the translation of "Frank" and to name the local money, until the use of the Euro in the 2000s.

However, rather than the ethnic name of the Franks coming from the word frank, it is also probable that the word is derived from the ethnic name of the Franks, the connection being that only the Franks, as the conquering class, had the status of freemen. In German, France is still called Frankreich, which literally means "Realm of the Franks". In order to distinguish from the Frankish Empire of Charlemagne, Modern France is called Frankreich, while the Frankish Realm is called Frankenreich.

Now here we're talking about cite-cite-cite-for-crying-out-loud-cite! Some of this might not only be original research, but speculation, also! Two Wikipedia-no-nos riddled into one! It seems like you only walk one paragraph or two down the article and bam! The poor thing is literally kissed with original research! Something has to be done! The original research label goes back till it's done!