If anyone is curious, as I was, there is some academic research on this, although not a lot. The most in-depth "palaeotypographical" analysis I have found was this [1] paper, which also seems to correct a long-standing assumption about the printing:

"Visual and historical evidence have led me to suggest that the font is the second pica roman of the Huguenot punchcutter Pierre Haultin [...] cast for Jaggard’s use probably around 1603 or 1608 by an unknown typefounder who likely inherited the matrices from Pierre’s nephew Jerome Haultin. The font was old and in poor condition when it was used to print the Folio, which supports the view that Jaggard and his pressmen did not see the Folio as an unusually important book."

[1] http://reedreibstein.com/assets/reibstein-first-folio.pdf