The stretch of the Middle Fork of the Flathead paralleling Highway 2 isn’t a particularly noteworthy fishing stream, but its upper reaches in the Great Bear Wilderness [1] are loaded with trout. These aren’t official fishing waters of the national park, so a Montana fishing license is required.
The raft companies [2] serve double duty as fishing guides.
Links:
[1] http://www.moon.com/destinations/montana/missoula-and-northwestern-montana/north-flathead-lake/hungry-horse/great-bear-wilderness-area
[2] http://www.moon.com/destinations/montana/glacier-national-park/west-glacier-and-the-flathead-river-middle-fork/recreation/rafting