When the French Revolution kicked off, nobles played a major part in it. Reformist members of the nobility like the Marquis de Lafayette and the Duc d'Orléans had been agitating for change for a long time, and many of them sat in the Second Estate (for the nobility) when the Estates General met. Eventually the three orders of the Estates General merged into a single National Assembly, which adopted the Declaration of the Rights of Man on Aug. 26, 1789. That declared in its first article that "Men are born free and equal in rights; social distinctions may be based only upon general usefulness" but didn't actually abolish nobility. The key moment for that happened in a decree dated June 19, 1790, that:

The National Assembly decrees that hereditary nobility is forever abolished. Consequently, the titles of Prince, Duke, Count, Marquis, Viscount, Vidame, Baron, Knight, Lord, Squire, Noble, and all other similar titles shall neither be accepted by, nor bestowed upon, anyone whomsoever.

Many members of the nobility emigrated out of France during the Revolution; some of those who remained were targeted by the Reign of Terror. But more than you might think simply remained on their country estates and quietly endured the Revolution. After Napoleon took power, he first issued an amnesty allowing emigres to return home (most took him up, with only the most intransigent opponents of the Revolution staying abroad), and then a few years later, after declaring himself Emperor, restored noble titles.

In addition to restoring the ancien régime noble titles, Napoleon also created a "new nobility" appointed by him for merit. These nobles predominantly earned their titles on the battlefield: 59 percent were military, and another 39 percent were domestic officials, while only 2 percent came from commerce, industry or the arts. Of these new nobles, a full fifth were already ancien régime nobility.

When Napoleon fell, the Restoration regime of the Bourbon family largely avoided overturning the apple cart. The first three articles of Louis XVIII's 1814 Charter of Government declared:

1. Frenchmen are equal before the law, whatever may be their titles and ranks.
2. They contribute without distinction, in proportion to their fortunes, towards the expenses of the state.
3. They are all equally admissible to civil and military employments.

While Article 71 said:

71. The old nobility resume their titles. The new retain theirs. The king makes nobles at will, but he grants to them only ranks and honors, without any exemption from the burdens and duties of society.

So under the Bourbon Restoration you had the old nobility, completely returned (including those final intransigents), forced to coexist with what they saw as upjumped parvenus. The nobility no longer had any of their pre-revolutionary privileges like exemption from taxation, a monopoly on officerships in the army, and the right to collect feudal dues from their peasants. They didn't automatically get back any land that was seized during the Revolution (though many of them purchased it back, with or without exerting social pressure on its new owners to sell). Old nobles tended to be somewhat poorer than they had been before the Revolution, but were still on average far richer than the average Frenchman.

Rather than rule by nobility during the Restoration, historians have capitalized the political-social order as a rule of the "notables" — a broad class based on wealth rather than heritage that included the old nobility, the new nobility, and some wealthy non-nobles. In historian Robert Tombs' words:

A jealous, quarrelsome, insecure and pushy conglomeration of ancient and not-so-ancient noble families, nouveaux riches, circumspect ex-revolutionaries... soldiers and officials, often decked out with Napoleon’s brand-new orders and exotic titles, formed the top of the socioeconomic pile... The Bourbon Restoration added to them the die-hard emigres, an awkward addition. These notables were the people with power in France after 1825; and their sons and grandsons held on to it at least until the end of the century.

Still, despite these divisions, as author David Higgs writes, "In society at large, nobles were considered to be alike, despite exclamations of disapproval in Legitimist salons.” (Legitimists were conservative old-line nobles devoted to the old order.)

The July Revolution of 1830, which replaced the conservative Bourbon King Charles X with his more liberal cousin Louis-Philippe, the Duc d'Orléans, changed little about France's social order. The new nobility and non-noble elites gained more social prestige, and the old nobility lost a little, but members of all groups of notables continued to be wealthy and prominent. (Louis-Philippe himself had bloodlines going back as far as anyone.) Some of the hard-core Legitimist nobles responded to the July Revolution by what was termed "internal emigration" — they left Paris and returned to their country estates, but the scale of this was modest and most nobles continued to reside at least part of the year in Parisian townhouses.

As to how ordinary people felt about the nobility during this time, there was certainly a minority who endorsed republican ideologies that noble titles should be abolished. (This included some actual nobles: in his later years the Marquis de Lafayette preferred to be addressed as "General Lafayette," and his conservative opponents delighted in calling him "Marquis" because it made him mad; the revolutionary official Lazare Carnot never used the title of "count" that Napoleon gave him.) But generally speaking, people tended to accept the way things were. Grievances were focused on more concrete issues than resentment of the nobility's mere existence, chief among them the ongoing watchfulness of peasants for any attempt by the nobility to restore the abolished feudal dues. Peasants knew that they were (by and large) economically better off with the conversion from a society of feudal dues to one of capitalist rents, and there are numerous reports of peasants using both legal and extralegal means to assert their rights. Peter McPhee relates one relevant example from the village of Lourmarin in Provence:

Jean-Baptiste Jérôme de Bruny... retained his extensive property but became the largest taxpayer, assessed for 14 percent of all taxes payable by the community. His tasque (one-eighth of harvested grain and olive oil), banalités and other dues were gone. The estimated value of his seigneurie had been about 16,000 livres, but by 1791 the taxable revenue from his lands was estimated at only 4,696 livres, a fall of about 70 percent. Relations between him and the village were henceforth those of property, labor and rent, suggested by the speed with which locals began litigation with 'citizen Bruny' after 1789. In the decades after 1800, they fought a protracted, successful battle with Bruny over his attempts to ignore ancient collective rights in his woods, 'dealing not with their seigneur but simply with another French citizen.

This shouldn't necessarily be taken as representative of how relations changed everywhere (the villagers of Lourmarin, among other distinguishing factors, were largely Protestants), and some areas of France retained more hierarchical social relations. More examples from McPhee:

In 1822, the villagers of Rennes (Aude) petitioned the prefect about the pretentions of his appointed mayor: 'The undersigned regard Monsieur de Fleury only as their mayor... and not as their former seigneur armed with feudal power and arbitrary dispenser of the product of their sweat. On the other hand, further west along the Pyrenees, nobles — including children — continued to assume social distance by a condescending use of tu [the informal second-person pronoun, used for speaking to children, among other uses] when addressing peasants. The comte de Comminges later recalled relations between his father and local peasants: 'The peasants were very attached to him, even though he treated them like negroes. Woe to whoever didn't remove his hat when speaking to him, for a blow with his walking stick soon knocked off the offending headwear. At that time, these dealings were accepted as quite natural.

"Of course," McPhee continues, "this was simply how a small boy remembered his childhood many decades later: we do not know what the peasants made of such behavior."

Despite France's many regime changes over the course of the 19th and 20th centuries, no future regime has repeated the original Revolutions abolition and suppression of noble titles. There are indeed noble families in France today, who retain some legal protections over the use of their name and title, even though any explicit or implicit privileges granted by such titles are now relics of the past.

Sources:

• Higgs, David. Nobles in Nineteenth-Century France: The Practice of Inegalitarianism. Baltimore and London: The Johns Hopkins University Press, 1987.
• McPhee, Peter. A Social History of France: 1789-1914. 2nd ed. Houndmills: Palgrave Macmillan, 2004.
• Tombs, Robert. France 1814-1914. Longman History of France. Harlow: Addison Wesley Longman, 1996.
• My past AskHistorians answers, "When Napoleon was defeated and Bourbons returned to power, did the French nobility manage to restore any legal privileges that they had lost during the Revolution?" and "Wasn't the power of French Ancien Regime even stronger in 1815-1848 than the reign of Louis XVI?"