"Monk" here is a variant spelling of "Monck"—specifically, George Monck, an English general instrumental in the restoration of Charles II. Aulard is essentially saying that even though Bonaparte and Sieyès permitted considerable expression of monarchical sentiment, neither had much interest in seeing the Bourbons actually return—much less being a major player in their restoration.

The comparison is not, however, original to Aulard—the idea that a "new Mon[c]k" would emerge to restore the monarchy was a hope of Napoleon's royalist contemporaries. Monck was a potent figure for royalists even before 18 Brumaire. In his 1797 Considerations on France, the conservative—and staunchly monarchist—philosopher Joseph de Maistre compared a prophesied Bourbon restoration to its Stuart equivalent (trans. Richard A. Lebrun): "Monk did not have to fight a single battle; everything was accomplished effortlessly and as if by magic. It will be the same in France."

After the coup, Napoleon was a natural choice as the next Monck, and the future Louis XVIII even suggested that he play the role (in exchange, of course, for the position of Constable under the restored monarchy). The comparison continued to be made by hopeful royalists, just as Napoleon was seen as a second Cromwell by staunch republicans. Napoleon himself does not seem to have entertained either comparison symbolically, just as he rejected both politically. An anonymous pamphlet on the Parallel between Caesar, Cromwell, Monck, and Bonaparte (c. 1800) sums up the future emperor's political role models quite succinctly: "Some superficial or malicious observers draw a connection between [Bonaparte] and Cromwell; some delusional fools hope to find a new Monck in him. France and Europe see a more striking resemblance with Caesar."

[Note: I'm not a specialist on this subject. Pretty much everything after the first paragraph is taken from a single incredibly relevant article: Yuki Kusuda, « Les fantômes des Anglais du xviie siècle au temps de la Révolution française », La révolution française 19 (2021): [link]. For more on the Parallel pamphlet, see Thierry Lentz, « Vers le pouvoir héréditaire : le “Parallèle entre César, Cromwel, Monck et Bonaparte” de Lucien Bonaparte », Revue de Souvenir Napoléonien no. 431 (2000): [link]. Both articles are freely accessible online.]