I was reading the Annals of St Bertin, and there's a very short section that describes the fate of some commoners who banded together to fight marauding vikings in 859:
The Danes ravaged the places beyond the Scheldt. Some of the common people living between the Seine and the Loire formed a sworn association amongst themselves, and fought bravely against the Danes on the Seine. But because their association had been made without due consideration, they were easily slain by our more powerful people.
Dani loca ultra Scaldem populantur. Vulgus promiscuum inter Sequanam et Ligerim inter se conjurans adversus Danos in Sequana consistentes, fortiter resistit; sed quia incaute suscepta est eorum conjuratio, a potentioribus nostris facile interficiuntur.
I've seen some secondary sources dispute the meaning of this paragraph, so I'll ask: Does it really say what it looks like, that the Frankish government killed their own people after they had fought off the vikings? What does 'due consideration' mean in a 9th century Carolingian context? Was it merely permission from a local lord? The King? Why were they slain instead of disarmed? Were they rebelling? Most importantly, is anything else known about this incident? Any other primary sources relating it?
Were there any other incidents of commoners banding together to fight invaders without due consideration in Europe? What was the legality concerning commoners' ability to defend themselves during the Viking age in the Carolingian Empire? What was their reasoning for keeping commoners disarmed and unmobilised (if they were so), even when under invasion?
And what would the writer of the Annals have meant by 'commoner,' exactly? Free peasants? Serfs? Merchants? Anyone who wasn't a noble or a part of the clergy?
This is a very strange passage. In Janet Nelson's edition of the Annals of St Bertin, she thinks that the vikings slew the the common people (p.89 n.1), but she doesn't explain how to reach this interpretation from the Latin text as is.
If I'm reading Nelson right, there's only six extant manuscripts, and most of these are late or fragmentary. Her discussion seems much fuller than that of Waitz, although Waitz does deviate from your Latin transcription, with sumpta for suscepta.
My gut is that this passage is either corrupt or was perhaps sloppy Latin to begin with. The dissonance between the common people (vulgus promiscuum) being described as both brave (fortiter) and reckless (incaute) casts the same action in both a positive and negative light. And the dissonance between "our greater strength" and the next sentence in which Charles needed to recover his strength ("King Charles recovered his strength," Karlus rex recuperatis viribus) makes it difficult to reason whether this is a moment of strength or weakness and whether we're talking about the strength of the Frankish people (eorum: plural) or the strength of Charles the King (singular, implicit in the ablative absolute referring back to Charles as a singular subject). So this whole passage is rather muddy.
My best guess is that the peasants actually slew the vikings: "But because their (the Danes') association had been made without due consideration, they (the Danes) were easily slain by our more powerful people (the commoners)." I think that the shades of meaning possible for conjuratio (association, conspiracy, plot) allows this interpretation, although the preceding phrase saying that the common people were the associating or conspiring group (conjurans) does make this interpretation somewhat awkward. It would nevertheless help make sense of the following sentence, since this reading would have the Danes catching Charles off his guard, the common people intervene and fend for themselves, and then Charles recovers his strength.
Alternately, as your translation suggests, the common people may have joined in defense but been slain by the vikings. In this case, nostris might be an error in the phrase "our greater strength." The author might have been attempting to distinguish their (the common people's) confederation against their (the Danes') greater strength, and simply biffed his pronouns. However, with or without this revision, this interpretation would rather problematically leave the Danes running around the Loire undefeated, and Charles hurrying off to fight his brother in the next paragraph.
One further option is that the common people allied with the vikings, which would make adversus an error but accord well with the overtones of conjuratio (conspiracy). The final sentence could thus be retranslated: "our greater strength (the Franks') easily overcame their (Danes + peasants) reckless conspiracy." The hint of insurrection here would better explain why in the next paragraph Charles needed to recover his strength.
So that's my impression about the passage as a whole. It's probably not the most satisfying, but I think it's important to note that given the Latin, it's really unclear what the author was trying to communicate in this passage. Regarding a few of your more particular questions:
"due consideration" isn't in the Latin. It's your translator's attempt to make sense of incaute, "off one's guard," or perhaps in this context "reckless" or "heedless." I think the author meant that someone made a poor assessment about the relative strength of forces (although whose forces he was referring to is difficult to know) rather than whether or not the commoners got permission to fight.
I'm not personally familiar with any other accounts of this, but you could also check the Annals of Fulda and the Annals of Xanten under 859.
Vulgus promiscuum is a very vague phrase and can't be better translated than "common people." I would expect that this included peasants, maybe merchants and craftsmen, maybe some low level aristocrats, and maybe even some slaves. I doubt it would include clergy and almost certainly no one of distinguished aristocratic rank who would typically be named in the Annals.