Dueling was seen as a privilege of the upper classes, and while anyone could, of course, physically fight a duel, much of the underlying nature of what makes a duel was intertwined with being a "gentleman" as opposed to a commoner:

If for common mortals in the Renaissance dying was a simple fact of existence, for the nobility there was la mort and la belle morte, signifying the honour and reputation that one’s death conferred upon the individual and his lineage; it was a terrestrial and worldly rather than a spiritual view of death. The gentleman’s insouciance towards death marked him out from the commoner.

A duelist was staking is life on his honor, and that amorphous concept was much more highly prized with the aristocracy of course.

But again, anyone can fight a "duel", even if it is two pig herders with pitchforks. If anything though, the observation you make is the reverse. A nobleman who killed his fellow Marquis in a duel would probably get a lesser sentence, generally, than were Jean the Mud Farmer to run through Jacques the Town Drunk. The French jurist Charles Loyseau observed that, "Gentlemen also have the privilege that when they happen to commit some crime they are not punished as rigorously as commoners", and in a crime committed to defend honor, which a Gentleman had much of and a commoner very little, this holds very true. Sometimes this was quite relative, since you aren't wrong that duelists were put to death in a number of cases, but even then, a nobleman would be spared the public hanging that a less titles person was bound for. The corpse might be displayed, but at least the act of death would be kept private. Beheading or garroting seems to have been more common.

Because of this possibility of harsh punishment, French duelists of that period would often leave Paris for their meeting, with Breton being especially popular due to a reputation for lawlessness due to a confusing matter of who had jurisdiction.

TL;DR: During the early modern period, dueling was often dealt with quite harshly, but commoners could face even harsher punishments, even if that is quite relative in some cases where we are speaking about the manner of execution.

All from "Blood and Violence in Early Modern France" by Carroll