BU means "
Brillant universel" or basically, "Brilliant Unicrculated" (I am fairly certain BU is also an English numismatic term, is it not?):
https://fr.wikipedia.org/wiki/Brillant_universel
BE means "
Belle épreuve", or basically, "Proof":
https://fr.wikipedia.org/wiki/Belle_%C3%A9preuve
What I do while contributing is put the corresponding English/French comment on a year line where I can see the other side has it.