Air carrier flight crew reported receiving a false localizer signal on approach to JAC that resulted in an early turn to final approach course; potentially putting them in conflict with terrain. Reporter disconnected the autopilot and corrected the course.

Narrative

We were at 14000 feet; cleared to proceed direct to DNW; cross DNW at 14000 feet and we were cleared for the ILS Z RWY 19 from DNW. I engaged approach mode; armed both autopilots and set the altitude to 8000 feet (matching the final approach fix altitude). The aircraft was operating in NAV mode with LOC armed; ALT CONST (14000 ft was FMGC alt constraint at DNW) mode with DES (Descent) and G/S armed.In the rough vicinity of the DNW 095 radial at about 8 DME the aircraft captured a FALSE LOCALIZER signal and began turning to intercept. This was WAY too early to intercept the actual localizer and would have put us on an instrument course directly toward terrain. Had a false G/S also been captured…it could have caused a descent into terrain.As PF I immediately disconnected autopilot and turned the aircraft back to track direct to DNW while the PM reset the approach and re engaged the autopilot.At the time we were in VMC; but had the aircraft been in IMC with a tired crew or without an attentive crew…it would have been very easy to allow the LOC capture to continue; leading to subsequent confusion and potential disaster.Cause: Aircraft automation and false localizer signalCompany procedures were followed; however a possible mitigation would be to provide guidance that aircrew delay arming the Approach mode until passing ZOSUV inbound to WOMRU. This would likely prevent a false intercept signal.