First, this is not "well-educated French acquaintences" so much as it is supporters of Melanchon's LFI political party, who explicitely campaign on the idea of ending the 5th republic to start a 6th where all problem would be magically solved.
Second, the reason I hate his proposal, is because he explicitely refuses to give any specific detail on what the 6th republic would be. He claims it would be "decided by the public" but there is no reason why a pre work couldn't be done BEFORE. In effect, he pretends to be saying "we will end the 5th for a better 6th", but what he's actually saying is "let's end the one we have now instead of fixing it, and replace it with something I will have the power to decide, you must accept to throw it away without knowing what you will get in exchange or how it will be made but trust me it will totally be better and I will totally let the people decide".
Our 5th republic might be flawed, but I'm not putting it in the trash without any idea of what we will get in return, that's brexit referendum level of flawed.
And I will always be weary of someone who claims to have a simple solution to a complex problem, on the condition that I give him power over me, especially if another condition is that I cannot know what said solution is before making my decision.
Third,
> the 6th in its history
Would be the 6th republic sure, but absolutely not the 6th "system of government", it would be like our 25th or something ?