TCASII WITH A FALSE ALARM CAUSED A WDB ACR TO CLB THROUGH THE ALT OF A NEARBY ACFT.

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DSNDING INTO PARIS WITH A DSCNT CLRNC TO 13000 FT. AT ABOUT 19000 FT OUR TCASII GAVE US AN RA TO CLB AT A MIN RATE OF 2000 FPM. WE INITIATED A CLB; AND AS WE DID SO; WE WERE ABLE TO SEE THE OTHER ACFT AT ABOUT THE 5 O'CLOCK POS AND 2 MI AND 300 FT ABOVE US IN LEVEL FLT. WE CONTINUED CLB AT 2000 FPM UNTIL THE TCASII RA WENT AWAY AT WHICH TIME THE OTHER ACFT WAS SHOWN TO BE 100 FT BELOW US AND DISAPPEARING FROM THE TCASII DISPLAY. WE NOTIFIED PARIS CTL OF OUR CLB AND THE TFC WE CLBED TO AVOID. PARIS ACKNOWLEDGED AND SAID THE TFC WAS 300 FT ABOVE US. THIS WAS A POTENTIALLY VERY SERIOUS NEAR MISS. 1) EUROPEAN CTLRS SELDOM POINT OUT CONFLICTING TFC. HAD WE KNOWN HIS BEARING AND ALT; WE WOULDN'T HAVE INITIATED A CLB. 2) TCASII COMMANDED A CLB INTO TFC THAT WAS APPARENTLY IN LEVEL FLT; EVEN THOUGH WE HAD JUST DSNDED THROUGH HIS ALT. 3) BY FOLLOWING OUR TCASII RA; WE ACTUALLY DECREASED THE SEPARATION WITH THE TFC. 4) WE DEVIATED FROM OUR ATC CLRNC TO AVOID THE TFC AND EUROPEAN ATC CTL DOES NOT ALLOW A DEV TO SATISFY A TCASII RA. WE DID NOT DECLARE AN EMER IN ORDER TO PREVENT CERTIFICATE ACTION BY THE FRENCH CTLR; HOWEVER; WE DO NOT EXPECT A VIOLATION TO BE FILED AGAINST US.