I'm not under the assumption that the entire class was wiped out obviously, but that it was severely diminished by the Republic, and subsequent revolutions as well. To this day, there are still people in France who hold noble titles, but what is the significance of this and is it in any way relevant in terms of public office or status?
In 1789, the French National Assembly ended the status of fiefs (and the peasant dues), subjected nobles to taxation, and stripped their special privileges such as seigneurial justice. Any dues that were considered contractual (as in not stemming solely from their title) were not abolished, and had to be purchased back by the tenant. So if a noble owned land outside his title, that land would remain theirs until the contract was purchased (20 years worth of dues, 25 if it was paid in kind with goods).
With those gone, their titles were merely ceremonial at that point. From the Declaration of the Rights of Man and of the Citizen: "Men are born free and equal in rights; social distinctions may be based only upon general usefulness."
In 1790, however, the Assembly abolished hereditary titles, which pissed off the liberal nobles who had accepted (and in some cases supported) the abolishment of their special rights and privileges. However, by this point, the angry nobles had no effective recourse.
However, Napoleon started granting titles under the First Empire. After the Empire was overthrown and the monarchy restored, the Monarchy restored the hereditary titles and kept titles granted under the empire (to appease Bonapartists). As time has gone by (with the monarchy being overthrown, restored, the second Empire, the restoration of the republic), noble titles are again powerless, and merely kept as a status symbol.