All three companies submitted preliminary bids last year for the deal with a value estimated at several billion dollars.
The reactor is intended for the Soviet-built Dukovany power station, which is located in the country's south and currently comprises four units.
"The bidders have placed a binding bid for a fifth unit at Dukovany and non-binding bids for another three units," CEZ spokesman Ladislav Kriz said in a statement.
The non-binding bids concern one Dukovany unit and two at CEZ's other nuclear plant in Temelin, also in the south.
CEZ currently runs six nuclear units at its two plants, which made up 37 percent of the country's total electricity output last year.
EDF chief executive Luc Remont said in a statement the company was "deeply focused" on the project.
"As the only vendor and builder of third generation nuclear technology in Europe, we believe that the long-term strategic partnership we are proposing will set a precedent for our continent and serve as the backbone for a more resilient and independent European nuclear industry," he added.
Comments from the other bidders were not immediately available.
The contract is due to be signed next year, with plans for the reactor to go online in 2036.
Russia's Rosatom and China's CGN had also previously expressed an interest in the bidding but Czech authorities said their proposals would not be considered "for security reasons".
Last year, Westinghouse won a bid to build the first nuclear power station in neighbouring Poland for around $20 billion, seeing off bids from EDF and KHNP.
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