For such an interior arrondissement, le Marais in Paris was spared from Haussmannization in the 1800s and still retains a lot of narrow, curving, Medieval streets. I can't seem to find any particular reason why it wasn't demolished and rebuilt like everywhere else, just that it was. My initial thought was that it had something to do with it being a Jewish area, maybe a poorer area, but I can't find any evidence supporting that. Thanks!
To start up with, "Marais" means a marsh or a boggy area in French. This area had -- at least until the XIXth century and the edification of the current setup of the Seine river banks (in the left bank most of the works date to the building of the train lines linking the Orsay station -- inaugurated in the 1900s, and in the right bank somewhat older). The quartier de l'Arsenal, in the southeast of the Marais, even had a third Paris island (the block currently containing the Morland building of the former Préfecture de Paris, currently rehauled as a hotel and social housing project by the city administration, and where yours faithful worked until 2016) called the île Louviers, bordered by a channel in the current Boulevard Morland's emplacement (it was filled up in 1843, and the island ceased to be an island)^1.
So generally speaking it was a relatively soft soil area, with a water table very close to the surface, which would have made it relatively difficult with late XIXth century techniques to reach the building heights found in Haussmanian arrondissements like the 8th or 17th.
On a social plan, the Marais was slowly emptied of its most wealthy inhabitants in the XVIIIth century : visiting Paris it is quite notable that most hôtels particuliers in the Marais date back to the XVIIth century with virtually no new building programs in prestige housing after the end of Louis XIVth reign : one of the last major projects in the area was the Hôtel de Rohan (now the national Archives, which has a very famous room decorated by Huet in singerie style), begun in 1705. Most major hôtels particuliers from the Louis XV and later period were in the Faubourg Saint-Germain (left bank, around the current Rue de Grenelle, for instance the Hôtel de Matignon where is now located the Prime Minister or the Hôtel de Lassay for the current President of the Assemblée Nationale) and Faubourg Saint-Honoré (right bank, around the current Rue du Faubourg Saint Honoré, for example the Palais de l'Elysée or the current-day place Vendôme, then place Royale, which was developped by financial fortunes of the Régence such as Poisson de Bourvallais from 1710, with an ensemble plan by Mansart, and became very sought after from the 1720s).
At the time of the Revolution, the Marais was no longer a fashionable area and had mostly been populated by craftsmen, workers and small merchants (which would be, with the population of the Faubourg Saint-Antoine in current day 12th arrondissement at the core of the events of the Revolution). A very lively portrayal of the population of impoverished intellectuals, workers, small traders and craftsmen, with a Jewish community and some provincial newcomers (Auvergnats) is given in the famous novel Le cousin Pons by Balzac, which happens somewhere in the 1820s-1830s and discusses the milieu of antiques dealers in that time (around very fun characters). It can be compared with the much more upscale parts of town around the Opéra and Saint-Honoré area where characters like Nucingen or Rastignac (once successful) live.
When Haussman came, this part of town was quite destitute and its formerly prestigious hôtels particuliers were in disrepair. Most of the extensive building programs he put in place were directed towards the most expensive parts of town where the development of his very specific city planning was justified from an economic standpoint. The core axes of development of Paris in that era and with Haussmanian design were the Avenue de l'Opéra axis, and further, around Saint Lazare, Europe, and the 17th arrondissement around Monceau (where major fortunes of the era like the de Camondo or Jacquemart-André would have lived) and the north of the 16th arrondissement (from the Champs Elysées into Passy, and then to the hôtel de la Muette area), which were closer to the main city amenities for the second half of the XIXth century bourgeois classes. Do keep in mind that this would be the areas developped in the Haussmannian era, as there would be significant further development copying his style well into the early XXth century.
Finally, the Marais was not completely spared by Haussman, in particular with the opening of the Boulevard Henri IV (linking the Île Saint Louis and the place de la Bastille in 1866).
The relatively destitute and disrepaired aspect of the Marais would remain well until the 1960s and A. Malraux considerable efforts to revitalize the neighbourhood and restore its magnificent Grand Siècle architecture (with the eponymous Malraux Law, allowing for fiscal deductions when repairing privately owned listed buildings for instance, which is still very much in place).
^1 : Gazette nationale ou Le Moniteur universel, vol. 21, p. 191, 3e colonne