"We had some good discussions, and I would expect that we will reach some kind of agreement by the end of the year," he told The New York Times in an interview.
Google did not immediately respond to an AFP inquiry on Schmidt's comments.
In the interview, the Google executive chairman appeared to maintain the company view that it does not owe a massive tax bill to France.
"Whenever you are dealing with government, you want to be very clear about what you will do and will not do," Schmidt was quoted as saying.
"And we don't want to pay for content that we do not host. We are very clear on that."
According to Paris-based news weekly Canard Enchainé, French tax authorities have made a billion-euro ($1.3 billion) claim against Google over financial transfers between Google's Irish holding company and its French unit for four tax years.
Google France told AFP this week that it had received no such tax claim, and that it complies with tax laws in all the countries in which it operates.
According to court documents, a Paris appeals court has rejected a request Google to invalidate the search and seizure of documents by French tax authorities.
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According to the court decision dated August 31, the French tax authorities believe that "the company Google Ireland Limited in practice carries out commercial activities in France using the human and material resources of the company Google France, without making the corresponding tax declarations."
Google reduces the amount of tax it pays in France by funneling most revenue through a Dutch-registered intermediary then to a Bermuda-registered holding Google Ireland Limited, before reporting it in low-tax Ireland.