French Prime Minister Manuel Valls said he would speak to President Francois Hollande about the proposal while an aide to Valls later said there was little new in Netanyahu's remarks.
"It can still be called the French initiative because you would host this genuine effort for peace," Netanyahu said.
"But here's the difference: I will sit alone, directly, with president Abbas in the Elysee (French presidential) palace or anywhere else that you choose. Every difficult issue will be on the table."
Valls is visiting Israel and the Palestinian territories to advance his country's plan to restart Israeli-Palestinian peace efforts.
He is due to hold talks in Ramallah tomorrow with Palestinian prime minister Rami Hamdallah.
Abbas has welcomed the French initiative to hold a meeting of foreign ministers from a range of countries on June 3, without the Israelis and Palestinians present.
Another conference would then be held in the autumn, with the Israelis and Palestinians in attendance. The goal is to eventually relaunch negotiations that would lead to a Palestinian state.
A Valls aide said the only new element in Netanyahu's comments was his mention of talks in Paris.
Palestinian leaders say years of negotiations with Israel have not ended its occupation and have pursued a strategy of diplomacy at international bodies.
Negotiations between the Israelis and Palestinians have been at a standstill since a US-led initiative collapsed in April 2014.
An upsurge in violence since October has killed 205 Palestinians and 28 Israelis. Most of the Palestinians killed were carrying out knife, gun or car-ramming attacks, Israeli authorities say.
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