Madame la Guillotine is the name Parisians fondly christen the guillotine, an apparatus used to behead the aristocratic enemies of the French revolution. It is a macabre nickname, but the revolutionaries speak of the 'fond embrace of Madame la Guillotine' with great satisfaction: they view the guillotine as an instrument of justice.
Accordingly, the guillotine was originally introduced as an instrument of execution by a Dr. Joseph Ignace Guillotin. He proposed that the guillotine would be a more humane method of killing than the usual axe or sword beheadings. In The Scarlet Pimpernel, executions were attended by many of the working class, who shouted and bayed for the blood of aristocrats. The 'tricotteuses' or old women who sat, knitting and sewing, beneath the platform, were presented as pictures of grotesque womanhood, witches who gloried in gruesome executions. Playing on this loathsome image of the ghastly tricotteuses, the Scarlet Pimpernel manages to evade Bibot with his handle of curly locks, supposedly hair from the heads of fallen aristocrats.
For more on the guillotine, you may be interested in:
Eight things you may not know about the guillotine.