Apartments are by far the most common type of housing available in Paris. From tiny student studios in a 6th-floor walk-up building to luxurious five bedroom apartments with wrap-around terraces, there is something in Paris for every taste and budget! The advantages of apartment living are numerous: they are ubiquitous and therefore easy to find, you are not responsible for building or grounds maintenance, they are located in absolutely every area of the city and its nearby suburbs, and they can be a very economical option as well. Disadvantages depend largely on the neighborhood and building. Consider whether you will have a concierge, an elevator, a courtyard garden and keep in mind that they can be noisier and less private than other forms of housing.
There are actually quite a few houses in Paris, from grand mansions to tiny workers cottages. They tend to be concentrated in the western areas of the city, such as the 16th, or the northern reaches of the city that have yet to be fully gentrified. You can also be surprised to find houses in artistic and eclectic sections of the 11th and 20th arrondissements. Houses, in general, are much more difficult to find, however, and therefore expensive relative to their size. In addition, they may be closer together and have smaller gardens than you might expect. That said, there are some truly lovely houses and cottages with splendid gardens, often in the nearby suburbs, that can be excellent value due to their distance from the city center. This distance can be an advantage or disadvantage depending on your perspective. Also keep in mind that you will most likely be responsible for the upkeep of the yard or garden of the house.
You might not have considered it, but Paris also has housing options other than apartments or houses. These include artist studios, commercial lofts and houseboats to name but a few. While obviously catering to a smaller section of the population, they are nonetheless available albeit limited in number. They may have fewer services and luxuries but may make up for it with loads of charm.