Hi Elaine! I've only stayed at 3 hotels in Paris:
1) Hôtel les Degrés de Nôtre Dame, 5th
2) Hôtel Valadon, 7th
3) Grand Hôtel Jeanne d'Arc

I love the 1st & the 3rd (the Hôtel les Degrés de Nôtre Dame is my absolute favorite but I'm not sure I'd call it a budget hotel, maybe some others would; prices range from 70€-160&euro
Here's their official website:
http://lesdegreshotel.monsite.wanadoo.fr/
And here's some stuff I wrote about them:
http://members.virtualtourist.com/m/tp/1015f4/
http://members.virtualtourist.com/m/tt/60b0e/#TL
http://members.virtualtourist.com/m/tt/60b1d/#TL

However, I'm looking into staying at the Hôtel Henri IV where the prices range from 23€-40€, I believe.

Here's its mention on Fodor's:
http://www.fodors.com/miniguides/mgr...erty_id=184591
Here's its mention on TripAdvisor:
http://www.tripadvisor.com/Hotel_Rev...de_France.html
Here's an old (1997) article from Metropole Paris:
http://www.metropoleparis.com/1997/7...9/mail239.html
And here are some write-ups from VT:
http://members.virtualtourist.com/m/tp/b0bfd/
http://members.virtualtourist.com/m/tp/d4557/
http://members.virtualtourist.com/m/tp/93a49/

thanks
23-40 euro worries me, so I'll let you be the pioneer. hope it works out

LOL, Elaine ~ deal!!