B767-300 CREW HAD MALFUNCTIONING FMS'S THAT ALMOST RESULTED IN A DIVERSION BEFORE THE ACFT ENTERED CLASS 2 NAV AIRSPACE.

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FMS'S MISSING ETA'S. AT CRUISE THE R FMS WAS MISSING ALL ETA'S ON THE LEGS RTE DATA PAGE AND THE PROGRESS PAGE. THE L FMS WAS ONLY MISSING THE DEST ETA ON THE PROGRESS PAGE. WE CALLED MAINT CTLR AND WORKED THE COMPLETE FMS FAILURE PROC. NO HELP. WE THEN TALKED TO MAINT CTLR AGAIN THEY ASKED US TO PULL THE FMS CIRCUIT BREAKERS AGAIN AND KEEP THEM OUT FOR 1 MIN (NOT THE 15 SECONDS THE PROC CALLS FOR). WE DID THIS. NO HELP. MAINT CTLR THEN ASKED US TO TRY THE CLOCK CIRCUIT BREAKERS. WE DID THIS AND GOT ETA'S TO ALL THE LEGS; BUT NOT THE DEST ON THE PROGRESS PAGE OF THE R FMS. WE WERE GETTING READY TO DIVERT TO JFK; BOS OR ORD IN BAD WX BECAUSE WE COULD NOT ENTER THE NATS WITHOUT 2 WORKING FMS'S. WE THEN TRIED ONE LAST THING. WE HAD ENTERED THE DPE4W ARR IN PARIS. WE DELETED THE VECTORS LINE AFTER PG520 AND THE L FMS SHOWED AND ETA TO LFPG ON THE PROGRESS PAGE. WE THEN DELETED THE ARR COMPLETELY AND GOT AN ETA TO LFPG ON THE R FMS. I DON'T UNDERSTAND WHY THE L AND R FMS'S EXHIBITED DIFFERENT PROBS BUT; I FEEL CONFIDENT THAT IT WAS ALL CAUSED BY THE DPE ARR. LATER WHEN WE ENTERED A DIFFERENT DPE ARR FOR LNDG E; OUR ETA'S DISAPPEARED AGAIN. WE ENDED UP ENTERING MOST OF THE ARR POINTS INDIVIDUALLY. THE MAIN POINT I BELIEVE SHOULD BE MADE IS THAT WE ALMOST DIVERTED DUE TO A DATABASE PROB. I BELIEVE THE FMS'S WORKED FINE ALL ALONG. THEY WERE SOMEHOW CORRUPTED BY THE DATA WE ENTERED. SECONDLY; I BELIEVE THE 15 SECOND TIME FOR THE CIRCUIT BREAKERS IN THE COMPLETE FMS FAILURE PROC IS NOT ADEQUATE SINCE MAINT CTLR TOLD US TO KEEP THEM OUT FOR 1 MIN.