Damn! You've succeeded to find a place to stay but what a surprise: there's no washing machine!
And you're becoming kind of "smelly" :D
This section is for you.

Laundry Services:

You will find a list of laundry services in Paris here [Fr].
The cost is approximately around 3 and 10€ (washing and drying).

La Machine du Voisin:

Literally "the neighbors' washing machine". Save money and get to know your neighbor's by using its washing machine. This is what offers this website [Fr]
It will cost you approximately around 2-4€ for a washing.