The move from Crédit Agricole could complicate UniCredit's bid to take over the smaller Italian lender.
Banco BPM shares spiked on Monday after the French lender Crédit Agricole announced it was boosting its stake in the Italian bank late last week.
Shares in Banco BPM were up over 2% in early trading, their highest rise since January 2016.
Crédit Agricole said on Friday that it had started proceedings to raise its stake in Banco BPM.
This would lift its ownership from 9.9% to 15.1%, subject to approval from Italian regulators.
The bank added that it did not intend to launch a tender offer for Banco BPM shares, meaning it won't urge shareholders to sell their stock.
This implies that a large-scale takeover isn't on its immediate agenda, although the French lender is currently Banco BPM's largest investor.
"This transaction is consistent with Crédit Agricole’s strategy as a long-term investor and partner of Banco BPM", said the French bank in a statement.
"It strengthens the solid industrial partnerships in consumer finance and in non-life, personal protection and creditor protection insurance, and highlights Crédit Agricole's appreciation of Banco BPM's intrinsic qualities, ie a solid business franchise with positive financial prospects."
Bid from UniCredit
The announcement from Crédit Agricole comes after Italian bank UniCredit launched an unsolicited €10.1bn bid for Banco BPM last month.
Banco BPM rejected the offer, stating that it undervalued the company.
The smaller Italian lender equally highlighted concerns about potential job losses, reduced competition in Italian banking, and UniCredit's expansion in Germany.
UniCredit has been increasing its stake in Germany's Commerzbank, a move facing fierce opposition from Berlin.
Banco BPM argued that a potential UniCredit takeover would expose its stakeholders to risks associated with the expansion in Germany.
The Italian state has said that it may block a UniCredit takeover of Banco BPM if it is not in the national interest.
The Meloni government has, however, informally approved Crédit Agricole’s plan to increase its stake in Banco BPM, according to sources from Reuters.
Banco BPM's expansion efforts
Also in November, Banco BPM launched its own takeover bid with an offer to buy asset manager Anima Holding.
This would allow it to diversify revenue streams as interest rates fall.
Rumours have also hinted at a merger between Banco BPM and Italian bank Monte dei Paschi di Siena (MPS), after Banco BPM bought a 5% stake in MPS.
A consolidated firm could hold the firepower to compete with larger lenders UniCredit and Intesa Sanpaolo in Italy.
The announcement from Crédit Agricole "changes nothing" for UniCredit, a spokesman for the larger Italian bank said in a LinkedIn post last week.
As of around 12 noon CET UniCredit shares were down 0.83% in daily trading, while Crédit Agricole shares were up 0.77%.