To start your search for your perfect Paris apartment, you need a good list. I constantly referred to one I came across on the Internet. It was simply called Apartment Rentals in Paris. It states that it is the most complete list of short-term rentals in Paris and that you can find anything you need. I believe them: http://www.parisapartment.com/.
It lists over sixty agencies and rates the website content as to images and descriptions. Other not-so-well-known sites that expatriates often use to find short term rentals are:
http://www.fusac.com/agencies.html and http://paris.franglo.com/classifieds/page.html
Inviting Crêperie: Île St-Louis
Having rented my previous apartments in the 7th from the owners, I had their insider info at my disposal. Since you may not have a contact like this, try the site VRBO (Vacation Rentals by Owner):
My experience with individuals that I have dealt with from this site has been very positive. They were kind, courteous, very helpful, and quick to respond to my email queries. Also even if the apartment is listed with an agent on another web-site, if you rent through this site, there is no agent fee as you are dealing directly with the apartment owners. The fee can be as much as 14% or more of your total rental cost.
Pay attention to the details and formulate and ask many, many questions. For example, check whether the rental fee includes utilities such as gas and electricity. This shouldn't be a deal breaker, but can add a few extra dollars to your stay. As can other details, such as whether there's a washing machine. Although I have met many interesting people dragging my dirty clothes to the local Laverie (laundromat) down the rue, having a washing machine saves countless hours (and Euros) better spent elsewhere in Paris.
If you are unfamiliar with what is included in an apartment rental in Paris, visit various rental sites and take some time to read the listings. This may help you come up with your own criteria of desires and must haves and what you are willing to forego. Then make YOUR list and start to sort out those attractive prospects that come close to meeting most of your criteria.
Once you have picked out an apartment or three that suit your criteria and sensibilities, you can take a virtual tour around the neighborhood. The French Yellow Pages (Pages Jaunes) website www.pagesjaunes.fr proves to be an exceptional resource: it has a photo of just about every street and building’s façade in Paris. Click on the English version of the site and select "Paris" from the "Photos of Cities" dropdown menu at the right of the page. Then zoom into the map. Or type in the address of the building you want to see. The photos are usually clear enough to give you a feel for the neighborhood, and the mini-tour may help you narrow down the area in Paris where you may wish to call home.