General Mallet's coup was well thought but he has one major problem : he said Napoleon had died in Russia. However, l'Empereur did not died as Mallet said : since he will return, Napoleon will probably try to retake his throne and probably succeeds because of two facts :
-Speed was one of Napoleon's strongpoints. Thus, if he returns fast enough from Russia, the restored Republic will be a very young regime and possibly not as popular as the First French Empire.
OTOH, Prussia and Austria will hear of the change before Napoleon does, since he is twice as far away. If they pull their fingers out, they may be able to nab the Emperor on his way back.
-Napoleon was very popular in France at the time. With such popularity, he can have the people on his side.
So, in the end, I don't think that will change history that much.
Besides, I don't think it mattered for the Allies wether they had to face Napoleon or the French Republic. They would still go for a Bourbon Restoration and a neutralization of France.
Could make a big difference to the peace terms, though. As I understand it, Malet announced his intention to withdraw from Spain, Italy and Holland. He didn't specifically mention Germany, but it makes little sense to hang on there while giving up everything else. Looks to me as if he intended to pull back to the Rhine and stand there. So France has a good chance of keeping those borders. Britain would have objected, but I don't think the Tsar would, particularly.
As for the Bourbons, from what I can gather[1], Malet's supporters included Royalists as well as Republicans. If worst came to worst, they could restore Louis themselves, for the sake of an easier peace, and get rid of him later if he proved intolerable. Given the frequency of regime change in France since 1789, whatever they set up was unlikely to last forever, so a few years of Bourbon rule needn't have been a big deal. That would certainly have been Talleyrand's attitude had he joined the new government.
One final twist. Iirc, a few days after the execution of Malet and his co-conspirators, Napoleon rode out to look over the battlefield of Malayroslavetz - and narrowly missed being killed or captured by a party of Cossacks. It would have been a grim irony if Malet's claims had become the truth - just too late to do him any good.
[1] My information mainly comes from Guido Artom's
Napoleon Is Dead In Russia - an excellent book, it covers the coup from beginning to end. If I may indulge in a bit of self-advertisement, I did a review of it on Amazon some time back.