RNZ reports in France and many overseas territories, Mr Fillon won a resounding victory in last weekend's run-off against Alain Juppé, but in French Polynesia Mr Juppé was the winner, backed by Mr Fritch and his party.
Mr Fritch told local television that discussions are needed between his government and Mr Fillon, who has proposed big cuts to the public sector.
He also said Mr Filllon has been vague about policies specific to French Polynesia and expressed appreciation that during the campaign, Mr Juppé paid a visit to Tahiti.
French Polynesia is highly dependent on transfer of funds to French administrators whose salaries in the territory are roughly double because of an indexation system.
Mr Fritch's anti-independence Tapura Huiraatira party is centre-right.