The Fall River is pretty darn snowy for access but with spring fed water also offers some good fishing conditions. Look for afternoon BWO hatches in a size 18 or 20, and small black Midges in a 22-24. This is 7x tippet time, so get a spool of that and you’ll fool more fish certainly. 
Knock Down and KD Duns, Film Critics, RS2, Captive Dun and Sparkle Duns are great flies now. 
Euro Streamers, especially Olive or Black have been our best producers on most days. 
Perdigons, Tungsten Micro May’s in a BWO Color, and the same with a 2 Bit Hooker. And of course Fall River fish love Eggs and Mops too.