The restoration of the ISF, replaced in 2018 by the IFI in which only wealth in the form of property is liable, is one of the demands of the Gilets Jaunes protesters.
ISF used to be payable by people who had total wealth of more than €1.3million after certain deductions such as 30% of the value of the main home, however the tax was calculated on wealth over €800,000, in rising bands. IFI, which removed many kinds of wealth from liability, was therefore claimed to be a 'gift to the rich' by some.
Government spokesman Benjamin Griveaux said the future of the tax was not under question at the moment - but said that all taxes are subject to parliamentary scrutiny.
He added: "If the evaluation is not the right one, the subject can be reopened. If a measure we have taken, which costs public money ... does not work, if something does not work, we are not idiots, we will change it," he said.
"It takes 18 to 24 months for the measures to take full effect. It was passed in December 2017. I think a good evaluation can start in the autumn of 2019.
"We want money to come back into the real economy, it's not a gift to the rich, it's about allowing our companies to benefit from French capital."
In the EU, apart from France only Spain currently has a tax on wealth.
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