French, who played the Rev Geraldine Granger, said she would have preferred the part of dim-witted verger Alice.
"I thought, 'How on earth do you play a central character who's so blooming good?'" she told BBC Radio 4.
The Vicar of Dibley's final episode, broadcast on New Year's Day 2007, was watched by 12.8 million people.
The episode marked the end of a 13-year run, which gave French her biggest success outside her comedy partnership with Jennifer Saunders.
Written by Richard Curtis, the award-winning comedy was based around a female vicar living in a rural Oxfordshire village.
But French told Desert Island Discs she had initially been dismissive of the main character.
"I thought 'Where are the flaws? Where is the monster in this woman?' That's what I understand comedy to be.
"Alice was a very funny character from the off. But anyway, he [Curtis] wouldn't let me play it."
The role was taken by Emma Chambers instead.
Despite French's reservations, the award-winning sitcom attracted guest stars including Johnny Depp and Kylie Minogue, and was remade in countries as far-flung as Kazakhstan.
But not everyone was a fan. The Bishop of Norwich, Graham James, an adviser on religious matters to the BBC, was unhappy with the Christmas episode in 2005.
"The jokes about Jesus were in pretty poor taste and the drunken performances at midnight mass lost touch with reality," he told The Guardian.
French's Desert Island Discs interview with Kirsty Young will be broadcast on Sunday 23 December.
She also spoke on the programme about the end of her marriage to fellow comedian Lenny Henry.
"Those last few months were pretty much like the first few months; we were good friends," she said.
"It was a tribute to the way we'd been married, the way we accomplished it".
Comedian Dawn French says she nearly turned down the starring role in hit sitcom Vicar Of Dibley because she did not think it was funny enough.