You've come to the right place — I run a podcast about French history starting in 1814, and over my first seven episodes have researched this topic thoroughly. Episode 1 in particular covers Louis's first Restoration and the mood of France at the time.
The Bourbon Restoration in 1814 came at a wild situation for France. The immediate cause was Napoleon's abdication in 1814, after the disastrous invasion of Russia, additional setbacks in 1813, and a spirited but hopelessly outnumbered defense of France when the Allies invaded in the spring of 1814.
At this point, France had basically been at war for an entire generation. Huge numbers of young men had died. Coastal areas had had their economies wrecked by British naval blockades, and now other parts of France had become battlegrounds. The country was exhausted, overtaxed and in debt, and all this reflected in the unpopularity of Napoleon now that he was no longer winning wars and bringing home treasure and glory.
The choice of Louis XVIII, younger brother of the guillotined Louis XVI, to be the new ruler of France was not guaranteed. There was talk about passing the throne to Napoleon's young son (with a regency by his Austrian wife), of crowning Louis's cousin, the more liberal duc d'Orléans Louis-Philippe, or bringing in a foreign prince to take the French throne. Ultimately, though, traditional French royalism was the most cohesive force both in and outside France, and the Bourbon royalists had the support of the British, where Louis had spend the last several years in comfortable exile.
Far from opposing Louis immediately, in fact, his return was greeted with spontaneous celebrations. Many towns issued proclamations praising Louis even before he returned. When he did re-enter France, landing at Calais in April 1814, a huge cheering crowd met him, unhorsed his carriage and pulled it through the streets. Some of this was genuine royalism, and some of it was opportunistic, but a lot of it also represented people cheering for what Louis represented: peace. The Revolution and Napoleon meant European war; it was commonly (and correctly) understood that Louis and the Bourbons meant a more pacifistic foreign policy. (It's also worth noting that not all of France was celebrating; Eastern France in particular was an area of Bonapartist sympathies.)
There was trepidation about the Bourbon Restoration, of course; people were terrified that they would try to undo the reforms of the past generation — restore feudal privileges, abolish the Napoleonic Code, and re-confiscate the biens nationaux, the lands the Revolution had seized from the Church and members of the nobility and sold to entrepreneurial French families. And in fact there were many so-called "ultraroyalists," including the king's own brother, the Comte d'Artois, who wanted to do just that.
But Louis himself had accepted that the ancien régime he had grown up with, and sorely missed, was gone for good. He was prepared to accept many of the past generation's changes. And the Allied powers didn't want to bring back the old regime, either. As a condition of backing Louis's return to the throne, they insisted he grant France a constitution limiting the power of the king. Louis agreed, and when he presented his constitution to the rump Napoleonic legislature, the mood in the room was relief at how relatively liberal it was compared to everyone's fears.
Of course, things didn't stay so rosy for the Bourbons. Over the next 10 months they would alienate many of the people who had cheered their return with a series of blunders, such as abolishing the tricolor flag under which many of the great military victories of Napoleon and the Revolution had been won, and backtracking on a promise to abolish unpopular Napoleonic taxes. (It turned out they needed the money.) So in March of 1815, Napoleon escaped his island exile on Elba and reclaimed his throne for a period known as the Hundred Days that ended at the Battle of Waterloo. After briefly considering other options again, the Allies again re-instated Louis as king.
This time around, the mood was much blacker. The Allied armies occupied France, sacking and pillaging and generally imposing their will and punishing the French. Louis's restored government purged thousands of disloyal officials, while ultraroyalist mobs in the south inflicted vigilante justice on their political enemies. Expressing support for Napoleon became a crime, even to the level of wearing the wrong type of flower pinned to your coat. This repression foreign and domestic helped keep opposition muted for several years until the Bourbon regime had established itself.
More broadly: lots of Frenchmen actually wanted the Bourbon Restoration. Those monarchists were split between the "Ultras" who wanted to turn back the clock to before the Revolution and moderates who supported a more modern constitutional monarchy, but both for different reasons backed the Restoration. The Restorations' constitution limited the vote to only the wealthiest 1 percent or so of the population, so the middle class — the most liberal group in society — had limited ability to exert their will through legal means. With the country exhausted from war, there wasn't any appetite for a new revolution, either, not for a good many years. Despite Louis's conciliatory efforts, the Bourbons never re-unified the nation. (And Artois would undo all of that work in a hurry once he took over as king in 1824.) But they were popular enough that it's not accurate to say they were imposing their will on a hostile populace through force of arms (outside, that is, of the immediate aftermath of Waterloo). The Bourbons brought peace, and economic recovery, as well as a certain royal legitimacy that appealed to a non-negligible slice of the population.
SOURCES
The full bibliography for my podcast contains a great many useful sources, but here are a few to start with:
What exactly are you asking? Why the people of France didn't oppose the Bourbon Restoration?
Are you asking specifically about the 1815 Restoration, or also about the 1814 Restoration?