Thing about Paris, and indeed other European countries, is that one can do a cheap "cheaply". This is coming from a person who lives in one of the highest cost of living cities in the USA, New York.
Thing to do is seek out hotels, hostels, or even apartment/home rentals (if one's group is large enough), that are out of the tourist center, and perhaps out of the way.
Great thing about most western European cities is that they have good,reliable and rather reasonable public transport. This makes getting about easy, fun and above all fast.
One can save on food by finding good local places, staying away from "tourist" traps, and or even finding a MacDonald's.
Must say one has a bias towards staying in priviate home/apartment as that is how I most always travel, thanks to a wide and generous group of friends, and it really does save money. Breakfast can be had at home, and lunches/snacks packed from things purchased at local shops or supermarket, much as one would do at home.
Another great thing about Paris, and France in general, is the museums, and such most always have special offers going. One purchases a pack of cards or just a card and usually it will give a discount to one or more places.
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