I have never undertaken a thorough review of French Revolutionary music, so I can't answer your question definitively one way or the other about songs specifically mentioning the guillotine. But popular revolutionary songs did endorse the violent judicial murder of counter-revolutionary individuals and classes.
The most famous and best example is Ça Ira, which you can hear here. One version of the song's lyrics (it was rewritten a number of times to account for changing events; its original lyrics were astonishingly specific to particular people and events of 1790) begins:
Ah ça ira ça ira ça ira
Les aristocrates à la lanterne
Ah ça ira ça ira ça ira
Les aristocrates on les pendra
That translates to:
Ah! It'll be fine, it'll be fine, it'll be fine
Aristocrats to the lamp-post!
Ah! It'll be fine, it'll be fine, it'll be fine
The aristocrats, we'll hang them!
Another stanza even hints at the guillotine, though it never actually mentions it:
Nous n'avions plus ni nobles, ni prêtres,
Ah ! ça ira, ça ira, ça ira,
L'égalité partout régnera.
L'esclave autrichien le suivra,
Which means:
We shall have no more nobles or priests,
Ah! It'll be fine, it'll be fine, it'll be fine
Equality will reign everywhere
The Austrian slave will follow him.
The first line could be taken innocently outside the context of a song calling for the lynching of nobles. The last line is really oblique, but "the Austrian slave" refers to Archduchess Maria Antonia von Habsburg-Lothringen, better known as Queen Marie Antoinette. When you remember that Marie Antoinette went to the guillotine after her husband, "The Austrian slave will follow him" becomes considerably more ominous.
Another Revolutionary song, the Carmagnole, which you can listen to here, also champions the violent overthrow and imprisonment of the monarchy, and the murder of their guards, though always in indirect fashion.
Monsieur Veto avait promis
D'être fidèle à son pays.
Mais il y a manqué,
Ne faisons plus quartier.
or:
Monsieur Veto promised
To be loyal to his country.
But he failed to be,
Show no mercy.
Which is somewhat ominous.
Other verses refer to the imprisonment of Louis and Marie Antoinette in the tower of the Temple, a medieval fortress in Paris. The song predates their execution, however.
The most explicit reference to violence comes in another stanza:
Les Suisses avaient promis
Qu'ils feraient feu sur nos amis
Mais comme ils ont sauté!
Comme ils ont tous dansé!
Which means:
The Swiss Guards promised
Not to fire on our friends
But how they jumped!
How they danced!
Which is again worded obliquely but is much more violent in context. The incident it refers to is the Insurrection of August 10, 1792, when a revolutionary mob stormed the Tuileries Palace and killed more than 600 members of the king's Swiss Guard, many of them after surrendering. "Jumping" and "dancing" are sick euphemisms.
These songs, with their championing of revolutionary violence, continued to be popular among the French Left for more than a century; a common description of revolutionary protest is that participants "danced the Carmagnole and sang Ça Ira."
I know this doesn't answer your specific question about mentions of the guillotine, and hopefully someone else can tackle that. But hopefully this provides a little more context about the violence in Revolutionary songs.