Untrue.
I've lived in Paris, London and SF and Paris is definitely the cheapest (even by the surface).
I'm paying $1100/month in Paris for a 300sq foot appartment (in a nice neighborhood). I was paying $3000/month in SF for a 400sq foot appartment...
I might be wrong, but I found the kind of room that $1000 pays for in NYC to be way nicer and larger than the one you can get for a similar price in Paris (though the usd/eur has increased 20% since I checked).