Traffic being vectored for a parallel runway crossed the final approach course and conflicted with parallel runway traffic.

Narrative

Aircraft X; an MO20; [was] IFR en route for visual approach to Runway 09L. Numerous slower VFR aircraft were being vectored to Runway 09L. I advised Aircraft X of slower traffic and to change runways to Runway 09R for a visual approach. Approximately ten miles from the airport; I asked Aircraft X if he had the airport in sight. He said; 'No.' I asked if he had the localizer setup for Runway 09R and [asked if he] could accept an ILS. He said affirmative and I then issued a clearance for the ILS 09R. His read back was correct and I assumed he would intercept the localizer and track the approach in. I also informed him of VFR SR20 traffic on the parallel runway. He acknowledged the traffic information. I then answered a land line on call. After the coordination; I observed Aircraft X had gone through the localizer Runway 09R and was merging with traffic on Runway 09L. I immediately exchanged traffic and Aircraft X said he had the traffic insight. I told him to maintain visual separation with him and to turn right immediately and asked if he had Runway 09R in sight. He did and I then cleared him for the visual approach to Runway 09R. During the first indication that Aircraft X had crossed the localizer; I also immediately informed Tower that I was turning Aircraft X and had visual separation. Tower advised that Aircraft Y was making evasive maneuvers. Had I not been coordinating with Approach; I may have noticed Aircraft X crossing the localizer. I had expected Aircraft X to intercept the localizer.