The cash consideration will be payable over three years and is subject to "strict performance conditions".
Planete Interactive and Webcontents merged at the beginning of 2005 and will become part of the Aegis digital network Isobar.
Planete Interactive creates corporate websites and e-commerce platforms for clients including Christian Dior, Pierre et Vacances, L'Oreal and PricewaterhouseCoopers.
Webcontents creates digital content across online and mobile for a range of clients including France Telecom, Michelin and the World Wildlife Fund.
The acquisition follows the group's move to buy Kirowski, a full-service digital agency based in Hungary last month, for a total cash consideration of up to €10m, payable over four years.
Robert Lerwill, CEO of Aegis Group, said: "Digital media is one of the most exciting areas we're in today. With Isobar, we're already ahead of the game in what we can do for our clients, and we're continuing to expand our offer.
"Planete Interactive and Webcontents are both high-quality businesses that will help us do just that, and we're pleased to bring them into Aegis."
The acquisition comes as uncertainty continues to hang over the future of Aegis. Earlier this week, Vincent Bollore, the French financier and Havas chairman, raised his stake in Aegis to 21.05% after the deadline for a takeover bid was given by The Takeover Panel.
WPP Group and Hellman & Friedman have now been given until November 25 to make a bid for the group, which owns media agencies Carat and Vizeum and market research firm Synovate.
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