An interesting example of this can be found in the 1424 Battle of Verneuil, between the Duke of Bedford (with largely English and Norman forces, I believe) and forces of the Dauphin Charles, including, Spaniards, Lombard Cavalry and, notably, Scottish forces under Douglas.

Contemporaries noted that this was a particularly fiercely fought battle and that, in particular, the Scots were slaughtered (rather than being taken prisoner after the English had won the battle). Jones notes that the tone of the battle was particularly unchivalric. The Dauphinist side had failed to keep the terms agreed for the battle (date, time etc.), and the English side was offended and smaller: they had perhaps 8,000 men compared with maybe 15,000 opposition. The new position at Verneuil was ideal for the Lomabrd cavalry whereas the original situation agreed had been better for the English, who would have fought defensively. The contemporary chroniclers note how offended the Duke of Bedford was at this slight. The involvement of the Scottish forces was even more offensive. A truce between England and Scotland had come into effect on the 1st May (I believe) which meant that the Scots would no longer fight with the French- but there was a loophole allowing Scottish forces already in France to stay. The English were offended at the Scottish presence.

This makes the levels of insults and chivalric challenges perhaps unusual, but it is not clear how far so. It seems that the English side and the Scottish forces, arrayed before the battle, hurled challenges, presumably with insults, at each other: this was to be a fight to the death, and the Scottish- oath breakers- did not deserve proper chivalric protocol.

So what were these challenges like?

One chronicle reported that Bedford mockingly invited Douglas to drink with him, and Douglas replied 'he would be delighted, since he had been unable to find him in England, and had come to France to look for him'. This was apparently a reference to a previous raid of 1417. The diplomatic context was therefore important.

I don't know of any more local insults that were recorded at Verneuil, though I imagine that some were far more vulgar. Somebody else has already mentioned Joan of Arc. According to contemporary chroniclers, she was twice called 'whore' or 'whore of the Armagnacs'. This seems entirely possible- yet it is also important to stress that Joan wasn't a usual combatant.

From what I've read, which mostly concerns elite communication (this was clearly far more likely to be recorded), insults were usually based on breaches of chivalric protocol. The Dauphinist murder of John the Fearless, for example, or the Burgundian 'betrayal' of the French crown. These were serious accusations that could change the ways that battles were fought (consider the slaughter of the Scots). More prosaic insults are less frequently recorded.