You would certainly have to uninstall McAfee to get avast to fully install all elements. I not sure if the same problem exists with McAfee (haven't seen much in the forums, try a search for McAfee and see), but NAV is notorious about the debris it leaves behind.
You could also visit their website and see if there any auto removal tools or advice on manual removal. If there are download them or the information, so you have it to hand. Then uninstall it using add remove, reboot and see if you can install avast without problem.
If you experience a problem then you could try the tools/information on manual removal and since you already have this to hand you won't need to go on-line to get it.