I am a HUGe fan of mostly non-religious choral music. I also like
there to be other instruments appart from the voice. What are some
great songs and great albums (such as the one from Les Choristes, the
french film)?

You can find recordings of familiar choral selections from operas,
many of which are well known and popular even among non-operagoers. 
They're usually accompanied by a full orchestra.

Archae0pteryx

The song 'Once upon a battle of life and death' from the Album
'Chronicles of life and death (Death- art version)' by Good Charlotte
is a pretty good song though its more opera like rather than normal
choral. Check it out anyways. Also
the song Listen to the Rain is something u might like.

The Kings singers have recorded some brilliantly entertaining party
pieces, close harmony choral pieces, mainly barber shop mens voice
stuff, but not many of these include instruments. Howvever, there are
lots of large scale works out there by well known composers. Most are
in fact sacred pieces but I would recommend the beautiful Symphony no.
3 by Gorecki, Polish composer who you may have heard of. It is a
mainly orchestral piece but with a gorgeous soprano voice on top of
some of the movements, listen to it in bed, it's beautiful.

British and american composers such as James Macmillan, Jonathon Dove
and others have composed folk song based choral works that are really
nice too. They are pretty easy to get hold of on compilation cds.
Check it out, do an internet search. Good luck.

Thank you very much music student! It helps a lot!