It seems unlikely, but there are some fine discount Paris hotels for under 100 Euros. They may not have all the amenities, but they do have clean rooms with en-suite bathrooms.

Grand Hotel Jeanne D’Arc
This is a charming, Paris discount hotel. It is located around the corner from a beautiful square with good restaurants nearby. This is a budget hotel that we can thoroughly recommend. Great area and a cute little hotel.
3 rue de Jarente
4th ARR
Metro: Saint-Paul
Tel: 01 48 87 62 11
Average price for a double room: €85
(See TripAdvisor Reviews)

Hotel de l’Esperance
38 rooms
This little Latin Quarter hotel is a real gem.  It offers a quiet and refined atmosphere and all rooms have direct telephone, individual safe, satellite TV, mini-bar , marble bath and/or shower with hair dryers. Breakfast can be taken in the garden-courtyard in summer. Although there is no-air conditioning, we highly ecommend this discount Paris hotel. 
15, rue Pascal
5th ARR
Tel: 33 01 47 07 10 99
Metro: Censier-Daubenton, Gobelins
Average price for a double room: €80

Grand Hotel Leveque
80 rooms
The Grand Hotel Leveque is located on the lively rue Cler, one of the last authentic market streets of Paris. All rooms have telephones with a private number, modem jack with direct line, color TV with cable/satellite, air-conditioning available only from June 15 to Sept. 15, a safe and hair dryer. This 3-star hotel is highly recommended because of the value and great neighborhood. Book early; it is a popular hotel.
29 rue Cler
7th ARR
Tel: 33 01 47 05 49 15
Metro: Ecole Militaire – La Tour Maubourg
Average price for a double room: €95

Residence La Sanguine
A simple 2-star discount hotel that has air conditioning and either a shower or bath. Family run, this central Paris hotel is friendly and gracious.
Rue de Surene 6
8th ARR
Tel: +33 (0)1 42657161
Fax +33 (0)1 42669677
Average price for a double room: €100

Le Quartier Marais
305 rooms
This budget hotel is located on a small, quiet street and just a two minute walk from the Republique square. Each room offers: cable and satellite TV, iron and ironing board, modem/data port connection, full bathroom, radio, tea and coffee-making facilities, phone,and WiFi. Given the good value and location of this hotel in the Paris Marais, we recommend it.
39 Rue Jean Pierre Timbaud
11th ARR
Tel: +331 4929 2020
Metro: Breguet Sabin
Average price for a double room: €84

Ibis Paris Bastille Opera
305 rooms
We generally like Ibis Hotels for their clean, simply decorated rooms designed for those on a budget. Located near Place de la Bastille, this is a modern 7-story discount Paris hotel with Wi-Fi- access and modern bathrooms. Handicapped rooms are available.
15 Rue Breguet
11th ARR
Tel: +331 4929 2020
Metro: Breguet Sabin
Average price for a double room: €99

Carofftel Gobelins
23 rooms
A stone’s throw from the Sorbonne this hotel’s location is convenient to the Latin Quarter. Recently renovated, this little left bank hotel offers modern and efficiently decorated rooms with all the modern conveniences. Triple rooms are available. Great prices for this fine discount Paris hotel.
8 Bis Avenue de la Soeur Rosalie
13th ARR
Tel: 33 0 1 4217 4747
Metro: Gobelins
Average price for a double room: €85

Moulin Vert
28 rooms
This is a 2-star, discount hotel that we heartily recommend. The Moulin Vert provides 5 floors of well equipped rooms with bath or shower, direct telephone line, cable TV, mini bar, individual safe, and radio. Reasonably priced continental breakfast is provided in either your room or in the breakfast room. Triple rooms are available and families are welcome.
74 rue du Moulin Vert
14th ARR
Tel:33 1 45 43 65 38
Metro: Alesia, Plaisance
Average price for a double room: €80

Derby Garibaldi
36 rooms
This central Paris hotel features single, double, triple and quadruple soundproof rooms, all equipped with direct dial telephone, individually controlled air-conditioning, desk, radio, mini-bar and cable TV. All the accommodations offer a private bathroom with tub or shower and hairdryer. Non-smoking rooms are available upon request. This 3-star discount hotel offers exceptional good value.
15th ARR
92 Avenue Garibaldi
Metro: Sèvres Lecourbe
Average price for a double room: €99

Utrillo
30 rooms
The Utrillo Hotel is conveniently located within walking distance to the Sacré-Coeur Basilica and the Tertre Square. The rooms are fully equipped with TV, mini-bar, direct dial phone, and bathroom including bath or shower. Note: there is no AC
57 rue des Abbesses
18th ARR
Tel: 33 1 42 58 13 44
Metro: Abbesses – Blanche
Average price for a double room: €79