The project, called "Centre Manche 2", will be France's largest-ever renewable energy installation.
TotalEnergies in a separate statement put the overall investment at 4.5 billion euros ($5.3 billion), making the deal the company's biggest French contract in three decades.
The offshore farm is to go onstream in 2033, and will take France's total wind energy production, either already in operation or in development, to 7.8 gigawatts, the energy ministry said.
France's four currently operational wind farms each produce under 500 megawatts, the same output level as the two wind farms currently being built.
France hopes to generate 45 gigawatts in offshore wind energy by 2050.
By 2030 already, French wind energy is to produce the electricity needs equivalent of two million French households, the ministry said.
TotalEnergies already runs offshore wind energy projects in Germany, Britain, South Korea, Taiwan, the US and the Netherlands as the group raise its investment in renewables.
Some 2,500 people will be employed during the three years of the Centre Manche 2 construction.
TotalEnergies has promised to spend 45 million euros on efforts to mitigate the environmental impact of the projet, and to ensure that it does not harm the local fishing businesses.
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