The original Franklin zinc mine is long closed and the deep pit is flooded. However, the Buckwheat Dump across the street is open to the public collecting. It's very picked through though without much good stuff coming out anymore. Fluorescent red calcite is still abundant as are small franklinite crystals. A bit of willemite as well, and odds and ends here and there.
Here are the hours posted on Franklin Mineral Museum's website for collecting availability:
March through November: Open weekends in March for all visitors; collecting available, weather permitting. Open Daily April through November Monday through Friday 10am to 4pm. Saturdays 10am to 5pm and Sundays 11am to 5pm.
If you want to collect in the area, the best suggestion is to go to the nearby Sterling Hill Mine in Ogdensburg. On the last Sunday of every month (excluding winter) they have collecting in the dump and also in the Passaic and Noble pits. The Sterling Hill museum staff does small level blasting and there is still good stuff able to be found here.