I would like to observe too.

Reminds me of the US civil war, all the euro powers sent observers, they were all like, we gotta see this shit. As that was the start of new weapons coming into use and all.

TL;DR: Yes, you would be welcome, and I think you would benefit from the experience. And it would be good to tell your stories to add to the public understanding of what is happening.

[edit] Saturday is the best day to reliably find a protest march. Start walking around looking for helicopters, listening for drums or sirens, and looking for where the people dressed in black are going. Unfortunately I don't know the hot spots in Paris, and it is a big city. In smaller cities like Montpellier, Lyon, Toulouse, or Bordeaux, it would be easier to find.

As a person who moved here from the United States within the past year, I find France to be very welcoming to people who are sincere in their intentions and respectful of the culture. I am that way, so I'm not sure where the boundaries are, but I imagine they are less receptive to the kind of blowhard behavior that some Americans are reputed to exhibit.

Coming to observe or march in the daytime protests would be easy, safe, and enjoyable. If you hear sirens and people start moving away from an area, walk calmly away. If you see clouds of tear gas or hear pops like big firecrackers (tear gas going off), walk calmly away. The police are professional and respectful if you listen and do as they say.

You can also sometimes walk peacefully through the police cordon into the area where the tear gas is, but be sure to listen for the officers to say no, and be prepared to let them search you if they ask. It is probably not as safe as in the main peaceful marches, but it has not been a problem for me yet, other than having my bag searched.

As for the protestors, 100% of them have been nice to me, even though my French immediately marks me as an immigrant. The daytime marches, where I spend much more of my time than in the tear gas, are borderline festive, though with a distinct air of grievance.

You'll improve the vibe as long as you behave like a leftist or a journalist~

Those things are hodgepodge from the get-go