I'm afraid I can't recommend an accurate film, except to recommend against Tom Holland's Islam: The Untold Story which came out recently and got a lot of attention. It makes a real hash of revisionist interpretations of early Islam, latching on to some of Patricia Crone's least accepted theories.

If you want something short and mass-media, I would give a listen to the In Our Time podcast on the topic, given that Hugh Kennedy and Robert Hoyland are two of the best scholars on this topic and are interviewed for the programme: http://www.bbc.co.uk/programmes/b00c5xzc