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It is PAI's first fundraising since a boardroom struggle in 2009 pushed out top management in favour of Lionel Zinsou, the former Rothschild banker who currently heads the buyout firm.
Zinsou has said he will step down in 2015, designating Chief Investment Officer Michel Paris as his successor.
PAI, which told an investor meeting in Paris on Tuesday it had secured a first tranche of 1.4 billion euros for its sixth fund, has benefited from a recovery in demand from U.S. and other international investors for exposure to Europe, where PAI focuses its investments, the source said.
On average, existing PAI investors have increased their allocation to the new fund by around 30 percent compared with previous funds, the source said.
After several tough years, buyout houses are now finding it easier to fundraise, with rising valuations and an improved flow of sales of portfolio firms helping to boost demand from yield-hungry investors at a time of record low interest rates.
Private equity funds closed globally last year raised $431 billion, according to data from research firm Prequin, up 13 percent on 2012 and marking the highest amount of capital secured in any year since the financial crisis.
Last month Nordic Capital raised 3.5 billion euros for its latest buyout fund, while in November Carlyle (>> The Carlyle Group LP) said it had attracted $13 billion for its U.S. private equity fund, $3 billion more than its target.
PAI has made four new investments in the last 12 months, including buying UK-based R&R Ice Cream from fellow private equity firm Oaktree Capital. It has also been busy on the exit front, selling a 9 percent stake in IT services firm Atos (>> ATOS) in November.
It expects to begin investing the new fund shortly, the source said.
($1 = 0.7324 euros)
(Reporting by Tommy Wilkes and Kylie MacLellan in London, additional reporting by Lionel Laurent in Paris; Editing by Alexander Smith and Mark Potter)
