Does anybody know car-hire small companies in Paris that accept debit cards?

Hertz does allow you to use debit cards per their website policy, you will just be subject to a credit check:

At most Hertz locations, debit cards (sometimes called check cards) issued under a VISA or Mastercard logo which draw funds directly from the cardholder's account may be used to qualify for rental. However, prepaid or stored value cards which have a VISA or Mastercard logo are not accepted to qualify for rental. When a debit card is accepted as form of payment, at the start of the rental, two (2) forms of identification must be presented. Debit Cards must have available funds for the estimated amount of the rental charges and any additional charges that may be incurred. Both debit cards and prepaid or stored value cards issued under a VISA or Mastercard logo may be used as a form of payment when you return the vehicle.

For credit check information when using a Debit Card click here.