Like many of the remaining noble families of the Ancien Regime ( because if a lot fled or were killed before/during the Revolution and the years following it, there still were a lot of nobles from the Ancien Regime ), the noblesse d'Empire slowly became notables alongside the growing bourgeoisie. However note that the noblesse d'Empire and noblesse d'Ancien Regime rarely mixed ( I mean married ).

So in fact they remained huge land owners, they also were the electors. For example, between 1836 and 1841 among the 60 wealthiest electors in France, 74% were nobles ( from the Empire or the Ancien Regime ). A lot of them started political careers, a little turned towards the industry ( but this was more a bourgeois path ). They also were very present during all of the 19th century in the administration. 73% of the prefects in 1893 were of noble extraction.

They also made careers in the army. At the beginning of the 3rd Republic, one general out of 3 was a noble. They also largely migrated to the countryside, bought some castles or huge mansions and settled there. This is where we can see that they truly became notables ( but not all of them ). Nobles mostly stayed out of some professions such as lawyers or doctors but were very present in the local political lives ( in the 1890s, many politicians at the top of the government were nobles ! Around 23% of the elected people's representative ( deputies,...Etc ) ).

If many nobles simply melted into the growing bourgeoisie class, not all of them did though. The values of the nobility were very different from those of the bourgeoisie.

Add to that that the nobility was, and is, not a united social class. Before the Revolution there were several '' classes '' among the nobility and during the 19th century the differences were very visible especially among the Ancien Regime nobility and the noblesse d'Empire. Plus there were a new class of fake nobles who cheated their way up ( falsification of documents ).

In a time when the nobility was truly facing an identity crisis ( after the Revolution ), nobles did not go all towards the same direction. The two nobility more or less mixed but remained very different from the bourgeoisie. Most nobles became notables and went to settle in the countryside where they turned to be respected members of the population due to their prestige ( being a deputy, a retired prefect,...Etc ).

Sources :

• Les grands notables en France (1840-1849) by Jean Tudesq

• Catalogue de la noblesse française by Régis Valette

• my teacher on this subject, though it does not count, I took some of the terms ( extraction, prestige,...Etc ) from her.

Modified from an earlier answer

Although the Bourbon Restoration engaged in a degree of purging and score settling, the Napoleonic nobility emerged out 1815 largely intact, albeit often demoted in status. Most of the Bourbon’s ire was directed at the apex of the Napoleonic aristocracy, the Princes and Dukes of the Empire. As with the Napoleonic nobility as whole, these were individuals were overwhelmingly military men such as the Marshalate, but there were some non-martial examples such as Cambacérès who was the Second Consul. However, the top of the Napoleonic pyramid were all men who owed their position to a personal relationship with the Emperor. Napoleon wrote to Cambacérès “I want no Dukes other than those which I have created or may create (...). If I make some exceptions with respect to the former nobility, these exceptions shall be extremely limited and shall only apply to historic names.”

Although the Bourbons executed Ney, they tended to be far more lenient to individuals who did not openly propagate a Bonapartist restoration after Waterloo. Although stripped of titles, these elites retained a sizable amount of their gifts and fortunes they acquired during their service to the Emperor. For instance, Davout retained some of his estate and the Bourbons eventually restored some of his titles despite the former’s unwavering support of Napoleon, even after Waterloo. Others such as Soult and Gouvion St-Cyr were able to regain very prominent positions within successive French governments.

One of the consequences of the Napoleonic system of coupling financial rewards with titles was that the corpus of the Napoleonic aristocracy was well-placed to marry into the old nobility of Restoration France. The result was a blending of the old and the new elite social groups within France. Although there was relatively little intermarriage between old and the Napoleonic nobility in the first generation of the Restoration, the numbers steadily climbed upwards in the reigns of Charles X and Louis-Phillipe.

One of the enabling factors for this transition was the Napoleonic regime's strong penchant for meritocracy (at least in theory) so there was always strong component of educated professionals within lower and middle strata of the Napoleonic aristocracy (the Barons and the Knight). These individuals were well-placed to expand their wealth and prestige during the Empire and became part of the foundation of the leading families of France during the nineteenth century. Although the Empire was infamous for its stifling court culture, Paris became an important social meeting place for these individuals and habituated them to the salon culture of the Restoration. Imperial schools like that run by Madame Campan, a former lady in waiting to Marie Antoinette, ensured that the children of the Napoleonic nobility were inculcated with the culture and values of the older aristocracy.

Ultimately, the Napoleonic legend of French gloire outweighed their questionable loyalties for many elites for the French state. Although there were outliers who still maintained Bonapartist sentiments. Those elite individuals that could not marry into wealth or transition into the new state apparatus became some of the founding members of the various secret societies and Bonapartist political parties. However, much of this nobility recognized that Napoleon would not return again and adjusted accordingly.

Sources

Bergeron, Louis. France under Napoleon. Princeton, N.J.: Princeton University Press, 1981.

Dwyer, Philip G. Napoleon and Europe. Harlow, England: Longman, 2001.

Natalie, Petiteau. “The Nobility of the Empire and the Elite groups of the 19th century - a Successful Fusion.” Napoleon.org. http://www.napoleon.org/en/reading_room/articles/files/nobility_empire_elite_arsenic.asp#ancre3

Woloch, Isser. Napoleon and His Collaborators: The Making of a Dictatorship. New York: W.W. Norton, 2001.

It was maintained by the 1814 charter. Most of French nobility is still Noblesse d'Empire.