I sympathise. I too looked for this option.
Naturally, with ADSL, you have to have a telephone line (or cable).
The closest you can get to 'ADSL without a telephone line rental' is to have Orange's VoIP service in conjunction with ADSL (and lose the ability to use the analogue phone line - Ligne Fixe), but Orange won't let you have just ADSL without their VoIP - though obviously, they could if they wanted to.
Alternatively, opt for Ligne Fixe + ADSL without add-ons (LiveBox, VoIP, TV, etc.), which is what I do, and then I use a SPA3102 in conjunction with a 3rd party VoIP provider for outgoing calls, e.g. voipcheap.co.uk (which means the Ligne Fixe receives calls free, but is not used to make any calls, except in a power cut).
There are non-ADSL Internet-only services, e.g. WiMAX, 3G, Satellite, 'sharing neighbour's wifi', etc.
Alsatis.com purport to provide WiMAX, but you will find many hurdles should you attempt to obtain it...