The increasing of his stake comes ahead of the Aegis AGM next week, where it has been reported that Bollore has agreed a deal that will give him board seats on the UK media and research firm.
Previously, Bollore has said that his holding in Aegis was a short-term investment, but he has continued to rapidly build his stake from 6% last August, taking it to 20% by October.
By November, his stake reached 25% and then he went quiet until March, when he started to slowly raise his holding again and said: "All options are open. We could strengthen our stake in Aegis."
At 30%, he will have to make an offer for the company. He was involved in talks of a three-way bid last year with WPP Group and US private equity partner Hellman & Friedman, which eventually came to nothing.
However, with Bollore again buying shares in Aegis, speculation has been renewed that he will make a bid for the company, which would likely see him merge Carat's media operations, Carat and Vizeum, with those of Havas, which owns MPG.
That would leave the way open for Sir Martin Sorrell, WPP chief executive, to take control of the Aegis market research business Synovate while retaining a stake in the media operation as well.
Speaking earlier this year at the World Economic Forum in Davos, Sorrell said: "The idea was that we would have a small stake in the media organisation and would buy Synovate, and we are interested in that."
Shares in Aegis haved edge up after the news, up 1.1 % to 136.25p. They have risen slowly since November when they stood at 118p after WPP and Hellman & Friedman declined to bid.
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