My thoughts on why Red Mage exclusive spells like Jolt/Impact and such are red, is due to being tied to Red Mages using their own living aether to generate their spells. Of course, due to the Alchemist questline, we know each individual has a unique color for their aether.

What I'd say that means, is that the original practitioners of Red Magic had shades of red as their own aether, and it was passed down this way via the Soul Crystals.

As far as Fleche and Contre Sixte go... In my honest opinion they are just, "hardlight" more or less. We've known and experienced the fact that aether can be made solid. Basically, for those techniques, the RDM envisions literal swords made of their own aether, and they become just that. By the by, mild spoiler, but according to the Alchemist quest line, the WoL's aether is blue.

If I had to hazard a guess as to why they were made blue and not red, it would be that they are rather reminiscent of the Armiger weapons from FFXV, which by Stormblood's release had been out for about a year. It features Noctis using spectral weapons of his ancestors. He has a dash-in, dash-out in the form of, "Warp." The Armiger weapons are all blue energy.

Of course, since its inception in the original Final Fantasy, Red Mage has always been tied to swords. Notably, broad and long swords even. The swords in Fleche / Contre Sixte are definitely more in line with long/broad style swords, rather than rapier. They actually bare a striking resemblance to the enemy, "Sword" from The 7th Saga, an Enix title from 1993.