They don't seem to be just "a bit fringe". If my French and my translator don't lie to me then "anarchisme de droite" is essentially the brain child of 1-2 people (one used it the other wrote about that person), the rest of it's "proponents" doesn't even know of their involvement in the "movement" or agree being grouped with that and isn't using the terminology.
Also the French article describes it as less of a political movement or a coherent ideology but rather of some "sentiment", trying to combine some individualist, anti-parliamentary and non-conformist themes with otherwise "traditional values" (whatever that means, but which apparently includes "aristocratic principles").
Despite the implication it has no ideological connection to individualist anarchism which focuses on the individual, but is nonetheless anarchist and does not promote the individual freedom that subjugates the rest, while right wingers usually do allow for such inequalities.
So in other words it seems to use "anarchism" not in it's defined political sense, but merely as some broad "against the system"-vibe. It should come as no surprise that anarchists reject their usage of the word as anarchism.
And a similar problem occurs for rouge-brun, red-brown or red fascism label. Where brown is the color of the Nazis and red that of the Communists (Socialists and historically also anarchists though they often go with black now) so to indicate a common base of the far right and the far left.
Most of the time that seems to be a pure exonym, meaning others call them that, no one calls themselves that. Some even go so far as to call that a liberal scarecrow to fight off both of it's enemies at once, despite the fact that it makes little to no sense.
Other examples include former "leftists" becoming far-right, though not keeping their leftist ideals, so they are just brown not red.
Some examples include left or right wingers trying to appeal to members of the other faction. Such as the KPD (German communist pary in Weimar Germany) praising a mythologized terrorist during the occupation of the Ruhr territory or far right groups pretending to be socialist.
Or last but not least movements that include far left and far right actors without a dedicated political group identity such as the yellow vest movement.
In neither of these cases does any actually coherent red-brown ideology exist. Nor do groups consider themselves red-brown or consider both simultaneous as part of their group identity. And attempts to appeal to the other group have been largely unsuccessful and short-lived.
So "rouge-brun" isn't really a coherent ideology but rather a label that is applied to things on a case by case bases.
The general problem is that none of the "ideologies" (rouge-brun or anarchisme de droite) makes the least bit of sense. The far left rejects social hierarchies, while the far right promotes them. So if you do both at the same time you're inevitably doing one wrong (usually the left part is ignored, though if the right promotes leftist values but doesn't follow through in their method you might also adopt the rightist label but do leftist stuff, though that is more rare).
So as neither of that makes any sense, it's likely futile to compare the ideologies and look for contradictions as their existence is already a contradiction and that didn't stop them. On the contrary if they were able to promote one such nonsense they might even do it again.
So the most likely connection would probably not be in terms of ideas but people, but so far I couldn't find a name that appears in both articles.
Though for obvious reasons if you go by purely semantic conclusions then you could label anarchism as far-left (doesn't really make sense as this faction forming and aiming for power isn't really a hallmark of anarchism, but from the perspective of the current system that would be the closest fit) and you would label idk the anti-semitic conspiracy theories and the aristocratic principles (whatever that means so likely nothing good) as far-right and so you could apply the exonym of rouge-brun.
Though just because that's how words work, that doesn't mean that it makes the least bit of sense in terms of what these words mean in the political context and you'd be doing anybody a disservice doing that.
PS: Also if you would do play these semantic games, then anarchism would no longer be exclusively far-left meaning you'd need to start anew. So no they just don't make any sense and are usually not self-descriptions or of such insignificant groups that an update of labels makes no sense.