Australia media reported that Stephen Brady's partner of 32 years was barred from an airport greeting party.
Peter Stephens was reportedly told to "wait in the car" rather than join Mr Brady on the tarmac to meet Mr Abbott.
Mr Brady offered to resign after ignoring the instructions, which Mr Abbott said were not from him.
The incident happened in April, as Mr Abbott was flying into Paris from Turkey where he had been marking Anzac Day.
He was not travelling with his wife, so under normal diplomatic protocol the receiving ambassador would be expected to welcome him without his or her partner as well.
The prime minister's office said he had been "very happy to be met by ambassador Brady and his partner when he arrived in Paris last month".
Mr Abbott said on Wednesday that there was "some issue at the level of junior officials and I don't concern myself with these things".
He said Mr Brady was "a fine servant of Australia, a really fine servant of Australia. He's a friend of mine, always has been and as far as I'm concerned always will be".
Opposition leader Bill Shorten, however, said that if the report was true Mr Brady and Mr Stephens "deserve an apology".
Australia largely has progressive attitudes towards homosexuality though it does not allow same-sex marriages.
Parliament voted down a bill to legalise it in 2012, and Mr Abbott has expressed personal opposition.
Earlier this week, some of Australia's most prominent business leaders came together to call for marriage equality.
The CEO of national airline Qantas, Alan Joyce - who is himself gay - said it would show young gay Australians that "they're not in some way second-class citizens".
Australia's Prime Minister Tony Abbott has dismissed as "trivia" a media row over the treatment of the gay partner of his ambassador to France.