A Firewall performs a different function to an Anti-Virus. Firewalls basically monitor the incoming and outgoing network connections of your PC(or network). They can allow or refuse connections to your PC based on specific ports or web addresses.
An Anti-Virus scans files and/or emails and websites to look for harmful applications.
So, unless an Anti-Virus is trying to send network traffic, a Firewall should not interfer with it’s operation. The only time a Firewall is likely to interfer is if the Anti-Virus software is trying to download updates through a route that is blocked by the Firewall. In this case you would open the Firewall and set it to allow the right port or web address.
If you are worried something is being blocked by the firewall, turn it off momentarily and see if that fixes your problem. If it does then turn the Firewall back on and set it to allow the program/port.
Don’t forget of course that a router can also block ports, and will come with most ports blocked by default.
To check your firewall status go to www.canyouseeme.org from the PC in question and enter a port number you believe to be open/shut and this site will tell you if it is open or not. Looking at your firewall and router you will be able to tell where the issue with said port is.