There are a number of conjectures being floated around on the internet suggesting that Napoleon had a longstanding interest in recapturing Quebec, though I don’t believe I’ve ever come across any works by major historians that would support this. I doubt seriously that Napoleon would have considered trying to regain any of France’s lost American colonies by the time he got into power in the early 19th century. Even King Louis XV would not have been so brazen as to risk breaking the 1763 peace treaty with Britain by attempting to take back even a portion of New France in the late 18th century. Then if you consider that France helped fund the American Revolutionary War, it would have been considered ludicrous to consider Napoleon would risk losing the neutrality the US provided France. Besides, by the time Napoleon came to power in 1800, it would have been impossible for him to mount a successful reconquest of Upper Canada (now part of Quebec) without getting into another costly war with Britain, which would at that point have allied with the US. Moreover, it would have been sheer suicide for the French to sail up the St. Laurence River by 1800, considering the combined might of both the British and American navies held by that point in time.

To put this into further context, even before the conclusion of the Seven Year War in 1763, especially after France’s resounding loss of New France (by 1760) to the British during the French and Indian War, the French seemed already consigned to giving up its American possessions. France had already signed with Spain the 1762 Treaty of Fontainebleau, in which the French were willing to cede its interests in Louisiana over to the Spanish in order to gain a needed ally in its fight with the British. In the end, the Seven Year War had been both politically disruptive and enormously costly for all involved. Neither the French, nor the British, had any interest in restarting that war. At the conclusion of it, France decided it had financially lost more than it gained by holding on to New France, thus it was more than willing, as part of the Paris Treaty of 1763, to cede lost territory to the British in order to hold onto its more valuable possessions elsewhere. This clearly shows that France was in no position to retake New France at any point between 1760 and 1763.

In addition, the French monarchy was in no financial shape to retake New France at any time between the Seven Year War and Anglo-French War of 1778-1783 (also known as the Bourbon War). The Anglo-French War became little more than a costly draw between those two nations. During that war, France was willingly aiding in various forms to the American colonists during their war of independence (1775-1783) against Britain, thus helping the Americans finally achieve independence in 1783. So, one can easily conclude from this, that the French foremost interest was in tying up British resources during the Anglo-French War, and secondarily thwarting British control of North America so that the Americans could achieve independence from the British. The French showed a non-interest within that intervening period towards making any direct claims on any of the remaining British territories for itself. As well, from the end of the Anglo-French War in 1783, until the beginning of the French Revolutionary Wars in 1792, France had fallen into political and economic turmoil, and would not have pursued any interest in Upper Canada. This again can be ruled out as a possible time-period in which France might have considered retaking those particular colonies from the British.

As we enter into the period of the French Revolutionary Wars of 1792-1802, France again indicated little interest in North America, as it was busy fighting a continental war in Europe. At this point it’s worth noting that Napoleon only graduated from the French military academy four years prior to the French Revolution in 1789 and didn’t even lead a French army out onto the battlefield (as a general) until 1795. The closest France came to showing any interest in the North American continent during this period, was when the US chose to default on its loan repayments to France. That resulted in the Quasi-War of 1798-1800. The French couldn’t even mount a serious navel attack on the US because the British had blocked its naval ports, and so the French had to rely on its own citizen privateers to harass American merchant ships. The result of this was the Americans started building an effective navy in earnest. By 1800 Napoleon came to power in France, and in 1803 agreed to sell off France’s last remaining possession, that being Spanish Louisiana, to the United States. So, there’s nothing in the chronology of that period to suggest that France, let alone Napoleon, could have had any serious ambitions to retake what remained of New France back from the British or Americans. Realistically, after the Louisiana Purchase, it would have been almost impossible for the French to even attempt to retake its former colonies without having New Orleans as its foothold. Even then, it would have risked a war against the combined strengths of both the US and British navies. Again, this time-period lends even less credence to the idea that the French had any plans to take back its colonies.

It now becomes clear that France had no real interest at any point, even during the Anglo-French War, to regain its foothold in North America, and even if Napoleon had contemplated retaking Upper Canada in the early 19th century, he faced a much bigger problem than starting a war with either Britain or the US. The French colonists of Upper Canada had always remained staunch monarchists, and so they viewed those who were involved in overthrowing their king during the French Revolution, including Napoleon, as their sworn enemies. Moreover, the French colonists enjoyed both peace and prosperity under the British, something they never truly experienced under the French. Thus, it’s likely Napoleon would not only have faced the British after landing on the shores of Upper Canada, but his armies would also in all likelihood have been facing the French colonists as well. Even more worrying would be the possibility of the US entering the conflict. It would be hard to believe that Napoleon’s fleet would have sailed into the mouth of the St. Lawerence without being soundly defeated by both the British and American navies. Thus, it would not be credible to suggest at that late stage, either during or after the French Revolutionary Wars, that Napoleon would have entertained the thought that he would be successful in taking back Upper Canada. This means the 19th century can effectively be ruled out as being a period in which France could realistically consider regaining Upper Canada.

Although I’ve only briefly discussed a few main points, I feel there’s clear historical evidence that after the French and Indian War, the French were never again in a position to plan a reconquest of New France. History is clear in that after the Seven Year War, the French considered New France nothing more than a drain on its resources. And certainly, Napoleon’s decision in 1803 to sell the Louisiana Purchase to the United States, clearly indicates Napoleon’s lack of interest in North America as a whole, let alone having any interest in what is now Quebec. Napoleon’s interests, not surprisingly, had always been drawn elsewhere in Europe. And finally, one would have a hard time making the case that after France’s loss in the French and Indian War, France was ever in any real position to retake Upper Canada. By looking at French history over those intervening years after France’s loss of New France, until the end of Napoleon’s rein, it’s hard to conceive of a point in that timeframe in which the French could have had a realistic chance of retaking any part of North America.

To conclude, after the loss of New France, the French were either too preoccupied with countering British aggression, or simply too involved in war on the European continent, to afford any secondary battle that could have retaken its North American possessions. Even by the time Napoleon had come to power, both the British and Americans were simply too entrenched within North America for Napoleon to seriously consider the possibility of retaking Upper Canada. Therefore, it simply isn’t plausible that the French, even under Napoleon’s leadership, would have drawn up a serious plan for the retaking of any part of New France, including what is now Quebec.

If you wish for a more detailed explanation to your question, the following links may be of interest:

https://www.thecanadianencyclopedia.ca/en/article/treaty-of-paris-1763

https://www.history.com/.amp/news/american-revolution-french-role-help

https://cdnhistorybits.wordpress.com/2016/06/28/how-did-napoleon-affect-canada/amp/

https://www.dorchesterreview.ca/blogs/news/napoleon-the-french-canadians

You may also find more information in this thread by u/enygma9753.

Although Britain had won Quebec in the 1759 conquest, France delayed the end of the Seven Years War until 1763 with the hope that they may yet acquire some colonial territories in the war to be used as bargaining chips in the eventual peace negotiations. This was a fairly common tactic during the 18th century.

Britain had captured France's highly profitable sugar colony, Guadaloupe. During the negotiations for the Treaty of Paris, France had the option to give up Guadaloupe and have Quebec/Canada returned to them, or keep Guadaloupe and give up Quebec and its 70,000 inhabitants.

France chose Guadaloupe. It was far more profitable. Quebec had once been very profitable in the 1600's due to the fur trade but by the 1750's it was costing the French Crown more to administer and defend the colony than the declining revenue it was bringing in.

The habitants aka French colonists in Quebec, after 150 years of living apart from continental France were more independent and less deferential to authority than their European cousins. They had endured and survived frequent attacks from the native Iroquois Confederacy, England and its New England colonists throughout their history, only to be forgotten when the peace treaty was signed.

There was a collective sense in Quebec of abandonment -- even betrayal -- over France's willingness to leave the colony to an uncertain fate under British rule. The colony's Catholic hierarchy urged them to keep the peace as British subjects and painted the emerging republicanism in the Thirteen Colonies as the path to anarchy, backed by the threat of excommunication of those who dissented.

This attitude prevailed in the lead up to the American Revolution, and the Patriots' heavy-handed treatment of locals during their occupation of Montreal and the audacity of the 1775 attack on Quebec City itself confirmed their mistrust of republican intents and anti-clericalism.

Napoleon's persecution of clerics and the church in France, as well as the ravages and excesses of the French Revolution alienated many in Quebec. There really wasn't a desire in the colony to return to France, when all they had seen was the chaos a revolution could bring -- they already had a preview, a front-row seat with the American Revolution.