The British government didn't actually back the proposals (although Lord Aberdeen believed otherwise, due to miscommunication). This means that there's always the risk that Britain deliberately breaks up negotiations. Then again, if Napoleon decides to eigerly embrace the offer as an "honourable peace" and openly suggests firm treaties of amity with all his continental rivals, I don't think they'll be willing to drag on the war just because Britain wants to do so. On the other hand, Britain will probably just demand something along the lines of "all your colonies are belong to us" as a condition for eventually accepting the peace deal.
Reputation-wise, Napoleon gets to be famous as a conqueror who bit off more than he could chew, but ultimately consolidated evert long-term strategic goal France had actually entertained for the past few centuries. He is less of a romanticised figure, but more respected as largely successful in the long term. There will be lost of people saying he's the best monarch France ever had, and he'll be less controversial. People will see him as "having finished the work of Louis XIV".
He lives long enough to hand over the throne to his son, and the Bonaparte monarchy lasts. France is confident in itself and has a far better strategic position towards Germany. Feeling threatened, the Germans may very well unite into a concrete nation-state, but a war against France would not be a smart strategy. In fact, considering Napoleon's peace with the continental powers, France and Austria may team up to keep southern Germany well out of Prussia's hands.
Internally, France will not see its cycle of monarchy-republic-monarchy-republic from OTL, but probably remain a monarchy (that increasingly becomes more and more constitutional). Many issues that plagued the French psyche in OTL ("Germany beat us! We are too weak! Our population is declining! We are a dying nation!") will probably never crop up in this ATL. We'll more likely be looking at a confident and secure France, which is widely considered the natural "heartland" of Europe.