Peaches' coffin was painted sky blue, with clouds and flowers along the side and a picture of her family and pets at the back.
Around an hour and 45 minutes after arriving, the hearse which had transported the socialite's remains left without the coffin.
Dozens of locals gathered outside the church, which is where Peaches married musician Tom Cohen, the father of her children, in 2012.
It is also where television presenter Yates married Geldof in 1986.
Yates' funeral was held there after she died from an accidental heroin overdose in 2000, aged 41.
There were bouquets and cards left outside the entrance to Davington Priory, Sir Bob's country estate next to the church, where Peaches grew up.
Written in chalk on the church's wall, a message read "RIP Peaches".
Mystery still surrounds her sudden death on April 7.
Her body was found at the home she shared with her husband and their two young sons, Astala, 23 months, and 11-month-old Phaedra, in Wrotham, Kent, after officers were called "following a report of concern for the welfare of a woman".
Former Boomtown Rats singer Geldof paid tribute to his daughter alongside his partner Jeanne Marine and Peaches' sisters Fifi Trixibelle, Pixie and Tiger, saying she was the "wildest, funniest, cleverest, wittiest and the most bonkers of all of us".
Kent Police said it was being treated as a "non-suspicious, unexplained sudden death".
An inquest is not expected until after the results of toxicology tests are known.
- PAA