Shares in TF1, which is aiming to merge with French TV rival M6, were up 1.4% by 0940 GMT while M6 shares were up 0.7%.
Kretinsky, who built one of Europe's largest energy groups through more than a decade of deals, already has stakes in Le Monde newspaper, French supermarket company Casino and UK supermarket Sainsbury, among others.
In an interview with French paper Les Echos published on Tuesday, Kretinsky said he backed the planned TF1/M6 merger, saying it would result in better content for viewers.
France's anti-trust watchdog is due to rule on the proposed TF1/M6 merger by the summer of 2022.
Other investments owned by Luxembourg-based VESA Equity, run by Kretinsky and his partner Patrik Tkac, include a 16% stake in Britain's Royal Mail, and stakes in German retailer Metro AG and Foot Locker.
(Reporting by Sudip Kar-Gupta; editing by Jason Neely and Louise Heavens)