The magazine reported that the bills concerned internet advertising and keywords for internet searches.
Despite a considerable presence in France, Microsoft paid only 32.2 million euros in corporate tax there last year, according to L'Express.
The French tax authority declined to comment, citing its policy to not discuss individual cases.
The US firm said only that it “acts in accordance with the laws and regulations in all the countries in which it operates, working in close cooperation with local tax authorities to ensure complete compliance with local laws.”
The 600 million euro figure is the second-largest amount France has sought in unpaid taxes from a high-tech multinational, after 1.1 billion euros recently sought from Google.
That case was similar as it concerned the billing of French clients via Ireland, which meant France did not collect revenue on the transactions.
However, in July a French court ruled in favour of Google in that case, considering that Google France didn't have a stable presence in the country and was only helping the Irish unit.
France's tax authority is appealing the ruling, but the government doesn't exclude a settlement.
US tech giants — including also Amazon, Apple and Facebook — have come under criticism for their tax optimisation policies, in particular using low-tax Ireland as their European headquarters and routing transactions through the country.
French President Emmanuel Macron campaigned on requiring internet firms to pay taxes to France on the business they conduct in the country.