I'll be going to Paris this July for two weeks with my mother, and I'm not sure which metro pass would be best to use for a reasonable price. We were planning on getting the Navigo metro pass, but I don't think that it's meant for tourists.
There are currently two types of magnetic Navigo passes: Navigo Personnalisée and Navigo Découverte. The former is available only to residents and those working in Île-de-France. The latter is available to everyone. I think the Découverte is the card you are looking for.
The linked website (in French) states that to obtain a Découverte you'll need a passport-type photo and 5€ for the cost of the card. It can be purchased at the RATP ticket points and in some participating shops.
Since you are looking to purchase a weekly pass note that these are available for purchase at the earliest on the Friday before the week starts, and the week goes from Monday to Sunday. The pass does not cover any consecutive seven day period. So make sure you do your calculations right before investing in a Navigo card. Your other alternative is an all day multi-day Mobilis ticket which is considerably more expensive than the weekly pass given the same number of validity days.