The first-half incident happened during last Saturday's Amlin Challenge Cup quarter-final between the clubs and resulted in Stade number nine Fillol being cited.
Fillol admitted a charge of committing an act contrary to good sportsmanship when he appeared at an independent disciplinary hearing in Dublin on Thursday.
Fillol's suspension will take into account the closed season, covering a 10-week period from April 6 until June 16 and then another four weeks between July 15 and August 11.
Independent judicial officer, England's Anthony Davis, found Fillol had been guilty of "an intentional, deliberate and grave act".
Davis decided the offence warranted a top-end entry point in terms of punishment and considered 26 weeks as his base before applying 12 weeks' mitigation.
"The judicial officer identified no aggravating factors," European Rugby Cup said in a statement. "And after taking into account compelling mitigating factors, which included the genuine remorse expressed by the player at the hearing, as well as his exemplary record and strong character references, the judicial officer applied mitigation of 12 weeks, before imposing a sanction of 14 weeks.
"The independent judicial officer heard evidence and submissions from Fillol, who pleaded guilty, from the Stade Francais Paris secretaire general, Cedric Boudarel, and from the club's legal counsel.
"The judicial officer also heard submissions from ERC disciplinary officer, Roger O'Connor, and considered written evidence from Peter Stringer. The Judicial officer found that Fillol had spat in the face of Stringer and that it had been an intentional, deliberate and grave act.
"He determined that the act warranted a top-end entry point from the IRB's sanctions for spitting, and considered that 26 weeks, from the available range of 11 to 52 weeks, was the appropriate entry point."
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