Is the construction still productive?
Other than anglophone and francophone, the other terms are very rarely used and are best avoided and clear forms such as "Italian speaker" used instead. In fact, I would probably avoid anglophone and francophone as well.

Are there additional commonly used terms?
No, anglophone and francophone are the only common terms. There are plenty of other terms, but I wouldn't use them. For example:
Allophone = Other language speaker (n m/f), Other language-speaking (adj) [i.e. with regard to one or more majority language(s)].
Anglophone = English speaker (n m/f), English-speaking (adj)
Arabophone = Arabic speaker (n m/f), Arabic-speaking (adj)
Fennophone = Finnish speaker (n m/f), Finnish-speaking
Finnophone = Finnish speaker (n m/f), Finnish-speaking
Francophone = French speaker (n m/f), French-speaking (adj)
Danophone = Danish speaker (n m/f), Danish-speaking (adj)
Gaélophone = Gaelic speaker (n m/f), Gaelic-speaking (adj)
Gallophone = Welsh speaker (n m/f), Welsh-speaking (adj)
Germanophone = German speaker (n m/f), German-speaking (adj)
Grecophone = Greek speaker (n m/f), Greek-speaking (adj)
Hellénophone = Greek speaker (n m/f), Greek-speaking (adj)
Hispanophone = Spanish speaker (n m/f), Spanish-speaking (adj)
Italophone = Italian speaker (n m/f), Italian-speaking (adj)
Lusophone = Portuguese speaker (n m/f), Portuguese-speaking (adj)
Néerlandophone = Dutch speaker (n m/f), Dutch-speaking (adj)
Polonophone = Polish speaker (n m/f), Polish-speaking (adj)
Russophone = Russian speaker (n m/f), Russian-speaking (adj)
Sinophone = Chinese speaker (n m/f), Chinese-speaking (adj)
Suécophone = Swedish speaker (n m/f), Swedish-speaking (adj)
Suédophone = Swedish speaker (n m/f), Swedish-speaking (adj)
Swahiliphone = Swahili speaker (n m/f), Swahili-speaking (adj)
Turcophone = Turkish speaker (n m/f), Turkish-speaking (adj)