The main area of controversy concerns new suits totally covered with polyurethane to aid buoyancy. The old suits only had polyurethane plates.
Fina said 136 other swimsuits needed to be modified to meet the requirement that "swimsuit material shall not be constructed to, or include elements or systems which, create air or water trapping effects during use".
The decision to reject the Jaked suit could create problems for the Italian hosts of the world swimming championships.
The Italy team is sponsored by Jaked, an Italian company.
Report - Hi-tech swimsuits polarise opinion
Frenchman Bousquet wore the controversial red Jaked swimsuit on Sunday when he beat Beijing Olympic hero Michael Phelps in the 100m final at the Charlotte UltraSwim.
Christian Donze, the French federation's technical director said: "Both swimsuits - the Jaked 01 and Arena's X-Glide - are not on the approved list. We're waiting for more information from Fina before making any statement."
Fina had already stipulated swimsuits should not cover the neck and must not extend past the shoulders and ankles, and limited the thickness and buoyancy of the suits.
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