French authorities have demanded that Google pays €1.6bn ($1.8bn; £1.3bn) in unpaid taxes.
The figure is substantially more than the £130m the search engine agreed to pay in back taxes to UK authorities.
However, France's AFP news agency reported that Google might be able to negotiate and may not pay the full sum.
The company's chief executive, Sundar Pichai, is visiting Paris and was due to meet the France's economy minister Emmanuel Macron on Wednesday night.
It is not clear if they will discuss the tax issue.
Earlier this month, French Finance Minister Michel Sapin ruled out striking a deal with the US company.
Google would not comment on reports of the tax demand and French officials said the matter was confidential.
The tax arrangements of international companies have come under close scrutiny recently.
Several have been accused of using legal methods to minimise their tax bills.
In Google's case, its tax structure allows it to pay tax in Ireland, even when sales appear to relate to the UK.
In January it struck a deal with UK tax authorities to pay an extra £130m in tax for the period from 2005, but that deal was heavily criticised.
Earlier on Wednesday the UK Public Accounts Committee (PAC) said the £130m settlement "seems disproportionately small", compared with the size of its UK business.
Europe's competition authorities have been examining whether some deals struck by big companies with national tax authorities amount to illegal state aid.
Starbucks and Fiat Chrysler were told they must pay back up to €30m (£22m) in taxes after European tax breaks were ruled illegal.
But the two companies disagreed with the ruling, and Starbucks said it would appeal against the decision.
Further investigations into tax deals, including those covering Amazon and Apple, are continuing.