This decision was passed at an evening meeting after four-hour debates, Europeiska Pravda wrote.
The final, amended wording of the resolution has not been published yet.
The French parliament's position was alleviated, in particular, regarding the gradual lifting of the sanctions.
There are 348 MPs in the Senate, 302 deputies voted for the resolution with 16 against.
At the same time, the document is of advisory nature, as it shows France's political positions, or recommendations.
The Council of the European Union is expected to decide on the extension of the anti-Russian sanctions in coming weeks.
Read alsoGermany, France confirm anti-Russia sanctions until full Minsk implementationAt a G7 meeting in May, French President Francois Hollande said he supports further sanctions.
