AN INT'L B757 PILOT REPORTS ERRORS CAUSED BY VERY SIMILAR INT'L FLT CALL SIGNS WHEN SPEAKING WITH BOTH ACCENTED FOREIGN CTLR AND US CTLRS.

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I WOKE UP 2 HRS EARLY AT XA30 AM LCL; UNABLE TO GO BACK TO SLEEP; AND I GOT READY TO DEPART. WE HAD A NORMAL TKOF WITH A LINE CHK PLT ON JUMPSEAT; THE IRO WAS IN THE FIRST CLASS CREW REST SEAT SINCE WE ONLY HAD 1 JUMPSEAT. WE CLBED TO FL330 WITH FRENCH CTLRS WITH STRONG ACCENTS. AT CRUISE FL330; I STARTED THE INFLT ACCURACY AND IRS RANKING PAPERWORK PRIOR TO XING THE N ATLANTIC WHEN ATC SAID 'ACR X CLB FL340 DIRECT TAKAS.' I ANSWERED THE ATC CLRNC AND THE FO CHALLENGED ME SAYING IT WAS NOT FOR US. I SAID I'LL CHK AGAIN AND HE INSERTED IT INTO THE FMC AND BEGAN A SLOW CLB. I CALLED ATC 4 MORE TIMES TO CONFIRM THE CLRNC BEFORE THEY FINALLY ANSWERED AND THEY SAID 'NO MAINTAIN FL330; THAT WAS FOR ACR X.' BY NOW; WE WERE FL335 AND WE DSNDED BACK TO FL330 WITH NO ACFT OR TCAS ALERTS IN OUR AREA. THEN ACR Y CHKED ONTO OUR FREQ. DSNDING INTO ZZZ AT FL200; ATC GAVE US A CLRNC 'ACR X CROSS XXXXX 14000 FT.' ACR X WAS RIGHT BEHIND US AND ANSWERED OUR CLRNC AND STARTED TO DSND. I CALLED ATC AND ADVISED THEM ACR X COPIED OUR CLRNC; HE TOLD THEM TO MAINTAIN FL200. WE READ BACK OUR CLRNC AND DSNDED TO 14000 FT. TWICE IN 1 FLT THE CALL SIGNS WERE MISUNDERSTOOD. OUR ACR CHANGED ALL OUR INTL FLT NUMBERS TO NUMBERS THAT ARE ALL VERY SIMILAR. THIS SHOULD HAVE NEVER BEEN ALLOWED AND WE SHOULD RETURN TO OUR ORIGINAL DISCRETE NUMBERING SYS. EVEN ACR Y HAD A SIMILAR CALL SIGN; THIS WOULD NOT BE ALLOWED BY US ATC AND THE FLT NUMBERS WOULD HAVE BEEN CHANGED PRIOR TO FLT. INTL ATC SHOULD BE NO DIFFERENT; ESPECIALLY WITH HVY FRENCH ACCENTS THAT ARE USUALLY HARD TO UNDERSTAND ANYWAY. WITH NO IRO ONBOARD; I HAD TO ASSUME HIS PAPERWORK DUTIES IN ADDITION TO MY OWN; DUE TO ONLY 1 JUMPSEAT. IF A CHK PLT IS ONBOARD DISPLACING AN IRO ON DUTY; HE SHOULD ASSUME THE DUTIES OF THE IRO TO SHARE THE WORKLOAD.