Expanding on my two earlier comments, the last archive link you posted offers the explanation on pages 344-345. Loosely summarized:
Regnault proposed a motion to introduce the tie breaking mechanism, all while suggesting the original idea stemmed from an earlier speech on the best ballot mode by de Mirabeau. Such a law, continues the explanation, would honor the constitution in that it ensures virtue gets rewarded.
The archive then sheds some light on what the intended meaning of virtue is. Namely, a patriarch figure. They considered giving a preference to married men, disrating former husbands who had divorced, and taking the number of children into account - all of which got rejected after a lively if polite debate.
Compte de Mirabeau was an opinion leader at the time and a great oratory. This other archive suggests Regnault was the MP of Nantes. (I'm suspicious that Regnault was the painter that lived at the time, because the latter was born and seems to have worked in Paris.)
I've honestly no idea if the rule is peculiar to France. But the French exported a lot of French ideas and ideals during the Revolutionary Wars, including e.g. its (then future) Civil Code in Malta, so it's at least plausible that you might find the same tie breaking rule in other European countries.
I would also point out, as noted in the Le Parisian article from my first comment, that the tie breaking rule doesn't apply to all elections. In particular it does not apply to the French presidential election, where the tie breaking mechanism is undefined. Were it to occur in practice, France's Constitutional Council would be called in to decide what to do, with two likely outcomes according to a jurist it's citing: recount with a more stringent eye to eliminate even more invalid votes (if memory serves, anything that gets in the way of a vote's legibility makes it invalid, but there presumably is some tolerance in practice to accommodate for e.g. dirty fingers or your kid playing with a pen while you're voting) or a straight up rerun of the election's round.
As to why that difference even within the country, it might be because direct universal suffrage for the president wasn't (re-)introduced until 1962 through a referendum, and the electoral college that it replaced didn't have or need such conflict resolutions. The electoral college's electoral process was, I would imagine, have been part of the Constitution from the 5th Republic, which had been written from the ground up by Debré, de Gaulle, et al., or been outlined while creating the 3rd Republic (which intended to explicitly get rid of direct universal suffrage, to avoid another Napoleon III). In contrast, the various levels of local elections that got introduced in France occurred through parliament, where the modus operandi would likely have been to copy/paste the language in existing electoral rules as a starting point and then edit. But, again, this is merely a hunch - it would need further research to confirm.