The company is in exclusive negotiations and expects the deal to be done but an agreement remains subject to certain conditions, including Picard's consultations with its works council.
Under the terms of the agreement, Aryzta will pay EUR446.6m (US$481m) for the stake. Aryzta would have the right to exercise a call option in three to five years to acquire the rest of Picard.
According to the Picard website, the company has over 920 stores throughout France. It also has 13 outlets in Belgium.
Bakery products supplier Aryzta said Picard’s 2015 revenue is EUR1.37bn. It also has a "March 2015 EBITDA run-rate" of EUR192m, Aryzta added.
Owen Killian CEO of Aryzta said: "The investment in Picard is consistent with Aryzta's strategy of consumer relevancy through diversifying markets and channel positioning. Picard has delivered consistent revenue, EBITDA and market share growth over the past forty years. It offers Aryzta the future potential to acquire a highly successful business-to-consumer platform focused on premium speciality food, which complements Aryzta's business-to-professional platform."
The deal comes just days after Aryzta raised over EUR404m from selling shares in Ireland-based agribusiness Origin Enterprises.
Killian added: "Picard is a highly predictable business and an ideal replacement for Aryzta's Origin holding, allowing Aryzta to strategically move up the value chain."
The private-equity firm had also been a shareholder in Aryzta. Lion Capital attained a slice of the business when it was formed in 2008 through the merger of Swiss baker Hiestand – in which the buy-out house owned 32% – and Ireland's IAWS.