AN AIRBUS ON APPROACH TO 35R OVERSHOT FINAL AND CONFLICTED WITH A B757 ON 35L APPROACH.

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THE ZZZ FINAL CTLR CLRED US FOR THE ILS RWY 35L. WE CAPTURED THE GS AND LOC AT 4000 FT AND WERE FLYING AN ASSIGNED SPD OF 210 KIAS. AT APPROX 3700 FT; THE CTLR SAID FOR US TO MAINTAIN 3500 FT BECAUSE TFC ON RWY 35R WAS CONFLICTING WITH US. THE OTHER ACFT ANSWERED FOR US AND THEN I RESPONDED TO THE CTLR AND OUR AUTOPLT WAS MANUALLY DISENGAGED AND WE LEVELED AT 3500 FT. I LOOKED OUT MY FO'S SIDE WINDOW AND OBSERVED AN AIRBUS HEADING TOWARD US AND HE PASSED BENEATH AND BEHIND US. THE CTLR SAVED THE DAY. THE CTLR CONTINUED TO STATE THAT WE NEEDED TO MAINTAIN 3500 FT BECAUSE HE WAS UNCERTAIN WHERE THE AIRBUS WAS GOING AND WE COULD RESUME THE APCH WHEN THE AIRBUS GOT STRAIGHTENED OUT. ACCORDING TO THE CTLR; THE AIRBUS WAS ON A VISUAL APCH TO RWY 35R AND WAS TALKING TO THE TWR CTLR. THE WINDS AT 3500 FT WERE FROM THE E AT 20 KTS AND I THINK THIS CONTRIBUTED TO THE AIRBUS FLYING THROUGH HIS APCH COURSE AND INTO OURS. THE VISIBILITY WAS PERFECT AND WE SAW THE AIRFIELD 30 MI AWAY. THE FINAL CTLR SHOULD BE COMPLIMENTED FOR HIS QUICK REACTION. THE AIRBUS SEEMED TO APPEAR FROM NOWHERE. NO TCAS WARNING WAS GIVEN. SUPPLEMENTAL INFO FROM ACN 780093: FO'S LEG ON OUTSIDE DOWNWIND. APCH ASKED IF WE HAD THE ARPT IN SIGHT. FO SAID HE DID OUT THE R WINDOW. I CALLED THE ARPT IN SIGHT AND WE WERE CLRED FOR THE VISUAL BY APCH. THE FO THEN TURNED TO AN APPROX 220 DEG HDG TO ABOUT 4 MI OUTSIDE THE FAF FOR RWY 35R. WE SAW TFC AT APPROX 2 O'CLOCK POS AND 1000 FT ABOVE AND 10 MI AWAY. I SAID HE IS GOING TO THE L SIDE AND THE FO ACKNOWLEDGED. I STARTED WATCHING THE NAV DISPLAY AS I COULD NOT SEE THE RWY BECAUSE IT WAS AT OUR 4-5 O'CLOCK POS. I NOTICED A 25 KT TAILWIND AND AT ABOUT 3 MI FROM THE FINAL APCH COURSE; I WAS EXPECTING A R TURN FROM THE FO. AT 1 MI; I SAID 'YOU ARE GOING TO OVERSHOOT.' AT THAT POINT; THE FO REALIZED HE WAS LOOKING AT THE L SIDE INSTEAD OF THE R. HE DISCONNECTED THE AUTOPLT AND PUT THE ACFT INTO A 40 DEG R BANK TURN AND WE GOT THE BANK ANGLE WARNING. I CALLED TWR TO LET THEM KNOW THAT WE HAD THE OTHER ACFT IN SIGHT. WE CORRECTED BACK TO RWY 35R AND LANDED UNEVENTFULLY.