PARIS - Qatar's sovereign wealth fund has called for fair board representation for all big shareholders in French media and publishing group Lagardere, echoing demands from investors such as activist Amber Capital for a shake-up at the group.

Lagardere, under fire for years from Amber over its governance and performance, has since become embroiled in a broader shareholder tussle involving some of France's richest businessmen, who are seeking to influence its strategy.

Qatar Holding, a subsidiary of Qatar Investment Authority and Lagardere's third biggest investor with 13%, said in a statement late on Tuesday that it considered it "legitimate that all significant shareholders be fairly represented."

The fund's rare public incursion in the increasingly bitter spat surrounding Lagardere, the owner of Paris Match, comes after demands by Amber and media group Vivendi, now the company's two top investors, for seats on the board.

Qatar Holding, which said it remained committed to Lagardere as a long-term investor, added that it had noted the request "by two core shareholders" and said it also reserved the right to be represented.

At present, the Qataris and other shareholders are not explicitly represented on Lagardere's supervisory board, which took on new members including former French President Nicolas Sarkozy this year.

Lagardere is controlled by chief executive Arnaud Lagardere through an unusual structure that gives him sway over the firm with only 7% of the shares.

Vivendi, controlled by billionaire Vincent Bollore, invested in the firm earlier this year when Lagardere's top managers sought help to fend off Amber at a shareholder meeting.

But Arnaud Lagardere has since also brought LVMH boss Bernard Arnault as an investor in his family holding company, while Bollore has switched sides.

Vivendi teamed up with Amber to ask for board seats, and the two have gone to court in France to try and trigger another shareholder meeting.

(Reporting by Sarah White, editing by Louise Heavens) ((sarah.white1@thomsonreuters.com; + 33 (0) 1 49 49 56 85;))