The email he received last Friday said the dimensions of the electronic wheelchair were "too big" to transport on the aircraft - which triggered a series of tweets from Mr Aikman, who has raised more than £400,000 towards research into his condition.
"Grrrrrreat! "Sorry sir, you can't take your legs on this @AirFranceUK flight" Thanks guys! #AirFranceFAIL", he tweeted.
He then added, "Sorry sir, your legs are too long - you can't fly with @AirFranceUK today".
However, budget airline easyJet confirmed it could accommodate the wheelchair and Mr Aikman and his partner flew to Paris on Monday.
He even received some celebrity support, with Harry Potter author J.K. Rowling tweeting him her best wishes for his honeymoon.
"The treatment I have had from Air France has been appalling," he told The Courier.
"Life isn't worth living without my electric wheelchair, but Air France has made no effort to resolve the situation whatsoever, it has just ignored me, has offered no alternative."
In a statement to MailOnline Travel, Air France said it would send an apology email to Mr Aikman and he would receive a full refund on tickets and baggage charges.
"We regret that it was not possible to accept the transportation of Mr Aikman's wheelchair due to the dimensions exceeding the capacity of the [Embraer 190] aircraft," it said.
"Air France had been in correspondence with the passenger trying to find a solution by possibly reducing the height of the wheelchair. However, due to the maximum acceptable height being 71cm this was not possible. Regretfully Air France was not able to convey this information to Mr Aikman quickly enough."
Mr Aikman was diagnosed with motor neurone disease in 2014 and depends on caregivers.
It is a terminal and progressive condition that attacks the motor neurones in the brain, leading to weakness and wasting. Eventually, those suffering from the disease lose their ability to walk, talk, eat, drink and breathe.
Mr Aikman launched a charity, Gordon's Fightback, which raises funds for research and awareness of the condition.
Last December he was awarded a British Empire Medal for his work.
- nzherald.co.nz