Napoleon named his campaign the Second Polish War and declared its aim to be the liberation of Poles living within the Russian Empire. In reality this was little more than political cover for his real aim: the reimposition of his Continental System (a trade embargo of Britain) on Russia. According to Andrew Roberts biography, if Napolean had been serious about the liberation of Poland, he would have established a Polish state in the territory he already controlled and in the process triggered a massive uprising of Poles in support of his campaign which may have been decisive.

His plan was to force a major battle with the Russian army and compel Tsar Alexander to negotiate. He intended to do this either on the frontier or in the territory to the west of Smolensk. He would then fortify Smolensk and Minsk and wait for the Russians to sue for peace. As it happened, the Russian army avoided fighting a major battle with the Grande Armie and Napolean was lured into pursuing them past Smolensk toward Moscow. This unplanned section of the campaign is where Napoleans forces would suffer most of their casualites.

He didn't really have one but that was not necessarily a bad thing. Owen Connelly puts forward the thesis with much evidence through Napoleon's contradictory orders and false battle reported that in most of his campaigns and battles, Napoleon operated without concrete plan, but instead made it up as he went. Understanding that war sas changeable and the flexibility to seize momentary opportunities was senior to all other talents, Napoleon was the "great improviser" in the field and said the only quality that mattered for general was energetic determination. His Russian campaign was no different, and he arranged a massive spearhead of almost half a million men to charge directly towards Moscow.

The comparison has been made by some Scholars of Napoleon a modern professional athlete. While he may have had a mental model of how the campaign was going to work made up in his head, he different from his enemies in the sense that he did not work out all the precise details before embarking on a campaign, as that could handicap him more than it helped.

Napoleon during the 1812 campaign had spent years languishing with his Habsburg wife in the palace in France, and numerou scholars comment on his inferior physical fitness and diminished spirits compared to his earlier days. Thus, many of the trademarks of Napoleon as an earlier frontline leader were gone. instead of performing impromptu inspections from horseback napoleon often rode in carriage and relied on his subordinates for work. Napoleon once said that if you wanted something done well, do it yourself, and he proved himself right when he did not check the exaggerated reports of his superiors of the fine condition of the men. Contra popular belief,f the winter did not undermine Napoleon - neone third of his massive host deserted or died on the march. He allowed Murat's cavalry to set the pace of the march, which was impossible for the infantry to keep up in. Heatstroke and exhaustion attrited his forces, while subordinates, to avoid blame, paraded their healthiest men in front of Napoleon during pre-announced inspections which gave them much time to prepare, carrying the impression that the men were doing fine. The Emperor had no clothes, but in the real word he could not rely on fiction's honest commoner voice to tell him that. Like many rulers, Napoleon benefited in his early career by checking on reports himself and auditing the "guarantees" given to him by his staff.

Napoleon maintained a flexible outlook in all battles, improvising and adapting as the battle took form. His armies fought several major battles on the road to Moscow, and were generally victorious, though his subordinates at each turn failed to encircle the Russian army as per his orders. They were not reprimanded severely, however, as failure to execute some orders was par for the course, and Napoleon, having fought dozens of battles, knew that. Once the French occupied Moscow, the campaign was as good as won. There is obviously no indication of what Napoleon's mental model is in his own words - numerous biographers go a long way to prove that Napoleon was a compulsive liar, and his memoirs cannot be taken for face value. However, records of his actions in his previous campaigns seem to suggest that Napoleon developed his own intuitive model for victory. Rout the main enemy force and capture the capital, and the enemy will sue for peace. Fail to do one of these two things, and the war will continue. This model held true in 100% of cases prior to the Russian campaign. However, Russia was an abnormality.

Most European countries had a heart, while Russia had many. As the old saying went, "half of France is between Paris and Brussels". In the age of Absolutism, monarchs concentrated the resources and investments of their countries in and around their capital cities. There was a definite "center of gravity" surrounding the capital. The Russian situation was different, however. The Duchy of Muscovy, as its name suggests, was traditionally based around Moscow. However, in the 17th century, Peter the Great built a new capital in St. Petersburg. However, St. Petersburg was a capital only in name and splendor. It was an isolated urban center that did host the court and ambassadors, but, as an economic asset, paled in comparison to the national center - the Tver-Moscow area - and especially to the South.

In the Second World War, Adolf Hitler differed with his generals in recognizing that the heart of Russia was actually not in its traditional power center, Moscow, but in the lands it had colonized. From the reign of Ivan III Veliky onwards, Muscovy and later Russia made great strides in disciplining the hordes of the South, opening undercultivated lands to Russian settlement. In 1815, Russia was not the population behemoth that it would be by 1890, and had a population still roughly equal to that of France. However, its population was heavily concentrated in Ukraine and South Russia, instead of in the North.

When Napoleon smashed the Austrian armies at Austerlitz after taking Vienna, it was over. When he defeated the Prussians at Jena and seized Berlin, it was over. When he defeated the Russians at Borodino and took Moscow, it was not over. Russia's brain was in Petrograd, its old heart was in Moscow, and its new heart was in the South - Kazan, Tambov, Astrakhan, Kiev, Chernhiv, etc. Unlike the Prussians and Austrians, whose subjects East of their capital were a collection of ethnicities of dubious loyalty, Russia could count on the active support of the peoples of the Volga, even if the line of communication with St. Petersburg had been cut.

Napoleon was initially confident Alexander would make peace, but he waited for weeks and no overture arrived. Thus, he began the march home. The Russian army, which was beaten but still in tact - much unlike the Prussian or Austrian in the previous wars - counterattacked at that moment, and had the advantage of being the pursuer. Retreat is generally harder to pull off than any other form of military operation, and Napoleon had begun the longest continuous retreat in military history.

Sources:

Connelly, Owen. Blundering to Glory.

Bennett, Lynch. The Grand Failure: How Logistics of Supply Defeated Napoleon in 1812.

Asprey, Robert. The Reign Of Napoleon Bonaparte.

From an earlier answer of mine

When Napoleon met Alexander I's envoy General Alexsandr Balashev in 1 July in Vilnius, Napoleon fumed at the fact that he had occupied a whole province of Russia without a major battle. "I'm already in Vilnius and I still don't know what we are fighting for," the Emperor is alleged to have said. Later in the interview, Napoleon ripped a window from its hinges and threw it into the courtyard below.

This particular anecdote is rather telling about Napoleon's endgame in Russia. Aside from the objective of bringing Russia to heel and back into the Continental System, there really was not much of a coherent strategy behind Napoleon's actions. He had hoped to destroy the Russian armies at the Polish frontier, but the Russian forces evaded the Grande Armee. Thus Napoleon was at a loss in this campaign and often let events play out as he became preoccupied with destroying the Russian army.

It is plausible that Napoleon intended to resurrect the kingdom of Poland if his invasion succeeded. His memoirs on St. Helena indicated that Napoleon would have put Józef Poniatowski on the throne, but this assertion should be taken with a grain of salt. The French 1812 treaties with both Prussia and Austria treated the Polish issue very gingerly and there is evidence that Napoleon's ardor for an independent Polish state had cooled somewhat by 1812. Napoleon only made very small steps to resurrect the Polish-Lithuanian commonwealth or grant Lithuania autonomy from the Russian empire. He did set up a provisional Lithuanian government and raised several Lithuanian military units. These efforts are counter-balanced by the presence of French military governors and the refusal of the French to announce an abolition of serfdom, which would have been a sign of a more permanent French reform of Lithuania. Military expediency underlay much of Napoleon's actions in Lithuania as the provisional government and the Lithuanian elite provided the French armies supplies and other forms of tribute.

Napoleon's treatment of Austria after 1809 does give something approaching a precedent as to how Napoleon would have treated a defeated great power. He browbeat the Austrians into surrendering slices of territory and paying a sizable indemnity, the Austrians were allowed to remain a power so long as it was allied to French interests. The existence of both the Duchy of Warsaw and the slightly enlarged Rheinbund states were to act as a check on Austria, but both these imperial entities were subordinated to French interests. In Napoleon's logic, these flanking satellite states would give Francis I no option but to hew to French leadership. The marriage to Marie-Louise was the carrot in this geostrategic partnership as it provided a personal connection between the Hapsburg and Bonapartist dynasties. Napoleon had a similiar attitude towards Alexander I, claiming that he had a personal connection with the tsar that was spoiled by Russia's corrupt ministers. His letters to the tsar, delivered by Balashev, emphasized that the two monarchs could still form a personal partnership. Napoleon flew into a rage when these entreaties were met with silence and at times threatened to raise a new Polish state and eliminate Russian power. While these tantrums do not speak well of Napoleon's character, an alternative explanation to them is that they were an exercise in brinksmanship as they would allegedly cow Alexander I into obedience. However, these threats were relatively empty. Any expansion of Poland would have increased tensions with the newly-formed Austrian alliance and many of Napoleon's diplomats warned him of this.

There are also reports that Cossacks captured dress imperial regalia during the retreat from Moscow. Again, it is unknown whether Napoleon wanted to symbolically refound his empire as a pan-European system after defeating Russia, but there were preparations for a set of new coronations in Rome for 1813. Given the recent annexations of Holland and Catalonia, the idea that Napoleon would have used a Russian triumph as a pretext to declare a rearrangement European political order is not outside the realm of possibility. But again, the lack of any clear indications on Napoleon's part makes this idle speculation.

In the end, Napoleon really did not have a very pragmatic or coherent grand strategy in 1812. Success against the Russians would have alienated his Austrian "ally" and provided a pretext for his Prussian "satellite" states, especially since the best check against Russian revanchism, a strong and independent Polish kingdom, would have eroded these shaky alliances. Russia itself was simply too big for Napoleon to partition or occupy for an extended period, as with Spain (and that itself went very poorly for the French). Napoleon had hoped the occupation of Moscow after the French victory at Borodino would somehow bring Alexander I to his senses and a negotiated end to the war, but this proved illusory. Moscow itself was not an initial goal when Napoleon crossed the Niemen but rather become something of a consolation prize after an arduous summer campaign capstoned by a slugfest. One of his few consistent ideas Napoleon entertained in 1812 was that French military power could compel Alexander I to see reason and accept a peace favorable to Napoleon's empire. The longer Napoleon waited for Alexander I to act bring an end to the war, the options Napoleon had to end the campaign narrowed and he found he no longer possessed whatever initiative he possessed when he crossed the Niemen.

Sources

Dwyer, Philip. Citizen Emperor: Napoleon in Power. Yale University Press, 2013.

Elena, I. Fedosova. "Polish Projects of Napoleon Bonaparte." The Journal of the International Napoleonic Society 1, no. 2: 98.

Gaidis, Henry. "Napoleon's Lithuanian Forces." Lituanus: Lithuanian Quarterly Journal of Arts and Sciences 30, no. 1 http://www.lituanus.org/1984_1/84_1_01.htm

Nester, William. "Why Did Napoleon Do It? Hubris, Security Dilemmas, Brinksmanship, and the 1812 Russian Campaign." Diplomacy & Statecraft 24, no. 3 (2013): 353-364.

Schneid, Frederick C. "Kings, clients and satellites in the Napoleonic imperium." The Journal of Strategic Studies 31, no. 4 (2008): 571-604.

Zawadzki, Hubert. "Between Napoleon and Tsar Alexander: The Polish Question at Tilsit, 1807." Central Europe 7, no. 2 (2009): 110-124.