The airline's request comes 24 hours after a dispute between the UK and France over landing rights at the French capital's southern airport was settled when France agreed to allow British flights into Orly from the end of next month.
Air Liberte is to lodge a complaint with the European Commission alleging discrimination by Heathrow against French carriers.
The complaint is expected to be supported by the French aviation authorities, possibly reopening the row over open skies in Europe.
Air Liberte's grievance is that it planned to start four daily flights between Orly and Heathrow from 30 June but has not been granted take-off and landing slots.
Rights given to British airlines at Orly are not reciprocated for French airlines in Britain, the company claims.
The European Commission said last month that the London-to- Orly route must be opened up, but the ruling was contested by the French.
The British Airports Authority, which operates Heathrow, said the issue was not intergovernmental but was about availability of slots at Heathrow.
BAA said that Air Liberte could take up slots at Gatwick, but had not yet chosen to do so.
Lufthansa, the German carrier, threw its hat into the ring yesterday, saying it also wanted landing rights at Orly.Reuse content