The fund will target €1 billion, making it the biggest the firm has raised if it closes on target.
Its last fundraising was in 2011 when it secured €850 million in a matter of months.
Chequers Capital, formerly the French arm of London-based private equity firm Charterhouse, typically invests in companies with an enterprise value of between €50 million and €500 million. The firm makes investments across a variety of sectors and has done deals across southern, western and northern Europe.
Since the firm was founded in 1972, it has grown its operations in Europe through the opening of an office in Munich and a joint venture partnership in Milan.
Chequers is among a number of well-known French mid-market firms looking to raise funds.
Other firms looking to raise capital include LBO France, which is targeting €850 million for its ninth fund; Alpha Private Equity, which is targeting €800 million, and Apax France, which is looking to secure €750 million, according to Preqin.
Dealflow in France has also picked up markedly in 2016 after a slow few years – a good sign for funds with capital to deploy.
Private equity-backed investments in France rose 87% through the first nine months against the same period last year; accounting for more than a fifth of all capital deployed by private equity firms in Europe, according to Dealogic.
In 2015, the number of buyout-backed deals fell below 200 for the first time since 2004, Dealogic said.