Seeing as how they'd just finished their very bloody revolution that had deposed the old regime, why did they so easily except another de facto monarchy? Especially when he even used the title "Emperor", which is obviously very evocative of the Roman Caesars. Were the people just tired of all the bloodshed, and decided that relative stability was worth it?
It's worth nothing that Napoleon chose the title of Emperor as an alternative to calling himself King - it's a bit ironic given the implications that Emperor has now, but it's on record that Napoleon chose the 'Emperor' title because he felt that it had less monarchical implications. He was thinking of the Roman Imperators and the connotations of election and military service that came with it.
Bear in mind France had never had an Emperor before, so in a sense he was distinguishing himself from the monarchs of the ancien regime.
Were the people just tired of all the bloodshed, and decided that relative stability was worth it?
Pretty much. He was a renowned French general who reformed France and, eventually, the rest of Europe, such as religious tolerance and the Napoleonic Code. When he installed himself, he named himself First Consul. This means that by the time he named himself "Emperor" (1804), he had already collected a name for himself. Although there were many people who disliked him, he pushed on to defend France from his rivals - the monarchy.