AN MD11 FLT CREW EXPERIENCED A DUAL FMC FAILURE AND TEMPORARILY LOST COM WITH CTLRS. THE FLT ENDED UP BEING INTERCEPTED BY MIL JET AS A PRECAUTION.

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AT CRUISE ALT (34000 FT MSL); FLT CREW EXPERIENCED A DUAL FMC FAILURE. THIS OCCURRED WHILE SELECTING ARR AND APCH POINTS IN THE MCDU. CREW MAINTAINED A LISTENING WATCH ON CTR FREQ AND 121.5 AT ALL TIMES WITH HEADSETS AND SPEAKERS ON. AFTER COMPLETING THE CHKLIST AND READY TO START DOWN; THE CREW QUERIED THE ATC CTR FOR A RADIO CHK; AS WE HAD NOT BEEN CALLED IN APPROX 15 MINS. WE WERE TOLD TO CHK FREQ. WE AGAIN ASKED WHAT FREQ WE SHOULD BE ON IF NOT THIS ONE. THEY ADVISED PARIS CTL. WE AGAIN ASKED THE SPECIFIC FREQ. THEY FINALLY GAVE US ONE. WE CONTACTED THAT FREQ AND WERE TOLD TO CONTACT ANOTHER FREQ. UPON CONTACT WITH PARIS CTL; WE WERE QUERIED AS TO WHY WE DIDN'T CONTACT THEM. WE TOLD THEM WE WERE NEVER SWITCHED OVER. THEY TOLD US WE WERE NOW BEING INTERCEPTED. WE VERIFIED THIS ON OUR TCASII. THE MIL PLANE SHADOWED US UNTIL ON APCH INTO LFPG. WE LANDED UNEVENTFULLY. WE NEVER; TO OUR KNOWLEDGE; HAD AN ALT INCURSION OR CLRNC PROB. SAFETY OF FLT DURING THE WHOLE EPISODE WAS OF PARAMOUNT IMPORTANCE. SAFETY WAS NEVER COMPROMISED.