BA is the only western european airline serving FRU, operated by British Mediterranean with a A321 (only european business class seats) stopping in Baku (doesn't sound like fun for an overnight flight)
Other "known" airlines serving FRU are Aeroflot, Turkish Airlines and China Southern.

If you want to max out *A miles and fly directly into FRU, you could go YYZ-PEK with *A, PEK-Urumqi with Air China (credit miles to UAL MP) and Urumqi-FRU with China Southern (credit miles to Delta/Northwest/Flying Blue)

You could go YYZ-...-ICN-ALA as well for more *A miles. ICN-ALA is operated by OZ only on thursdays.

Another option would be a *RTW YYZ-FRA-ALA-ICN-...-YYZ (maybe the cheapest option as well)