Emmanuel Macron told the Andrew Marr Show the £18bn project in Somerset was "very important" for France and EDF, which is 85% owned by the French state.
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Mr Macron said work still needed to be finalised but he hoped something would be signed with UK officials this week.
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Greenpeace said alternatives to Hinkley Point were "increasingly attractive".
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EDF has yet to outline how it will fund the project.
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The costs are rising, the problems are mounting, and the opposition in France is growing\r\nJohn Sauven, Greenpeace director
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In October last year, it agreed a deal under which China General Nuclear Power Corporation (CGN) would pay a third of the cost of the project, in exchange for a 33.5% stake.
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But EDF has been struggling to find the cash for its remaining 66.5% stake and the cost of the Hinkley Point project now exceeds EDF's market value.
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All you need to know about Hinkley Point
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Nuclear power: The future or the past?
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Hinkley Point: Pressure grows at EDF
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The company's financial director resigned over the cost in March and last week the French Energy Minister Ségolène Royale said it should be delayed.
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But Mr Macron told the BBC: "We back Hinkley Point project, it's very important for France, it's very important for the nuclear sector and EDF.
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"Now we have to finalise the work, and especially the technical and industrial work, very closely with EDF, with the British government, to be in a situation to sign in the coming week or more."
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Asked whether he thought the deal would go ahead, Mr Macron added: "That's my view, and that's our perspective, because I think it's very important for our commitment to nuclear energy."
