The fundamental problem is, imho, the link to the Nation. The PCF is historically internationalist and they tend to prefer referencing class struggle rather than French identity. Mélenchon has chosen the opposite way; his rallies were full of tricolor flags and he sung the Marseillaise with the crowd, something a PCF candidate would never do. Both are building their discourse around historical references; the Labor movement for the PCF, and the French Revolution for la France Insoumise.
Guess which strategy works best?
From what I 've read the sources of inspiration for Mélenchon and la France Insoumise were certain Latin American political movements (such as Rafael Correa's "civic revolution" in Ecuador), Bernie Sanders and Podemos in Spain. There are obvious differences between countries and FI is neither Podemos nor Correa's party, of course. Anyway that appeal to the French Revolution and its symbols concurs with the appeal of Latin American leftwing populism to the "people" and the "motherland". There is some influence of leftwing populist theorists Ernesto Laclau and Chantal Mouffe. The latter wrote a book with Ïñigo Errejón from Podemos which title translated into French is
Construire un peuple.
https://www.editionsducerf.fr/librairie/livre/17946/construire-un-peupleAnd there was that March for the VI Republic with the presence of Chantal Mouffe
http://www.lemonde.fr/politique/article/2017/03/18/entre-bastille-et-republique-melenchon-reussit-son-pari_5096932_823448.htmlWhile in 2012 Mélenchon made calls to assemble "the people of the left", in 2017 appealed to "the people" without additives and the red flags were much less visible. It's obvious that people in the PCF couldn't be happy with that, but FI got seven million of votes.
Another question is how arrogant Mélenchon is and how stupid and suicidal has been for the Left running separate lists in the legislative elections (it looked that it saved face somewhat by winning 17 and 10 seats, but it's indisputably a poor result). Even Pablo Iglesias (who is a bit of an arrogant prick in my opinion) pales in comparison in what regards personality cult and sectarianism.