Monitoring a FortiGate 60D firewall using Nagios XI

Monitor means getting updated information. Hence you have to use SNMP. FortiGate is SNMP agent. Nagios XI is an SNMP server. You have to configure community string which is considered the security password for SNMP. When you configure it on both sides, Nagios XI will query FortiGate for the status update. To get a real-time update sent to Nagios XI when the event happens, you have to enable on FortiGate the types of traps to be sent.

SNMP Monitoring With Nagios

https://www.nagios.com/solutions/snmp-monitoring/

How to Configure FortiGate SNMP Agent for Monitoring

https://community.fortinet.com/t5/FortiGate/Technical-Tip-How-to-Configure-FortiGate-SNMP-Agent-for/ta-p/196866

https://docs.fortinet.com/document/fortigate/6.2.0/cookbook/62595/snmp

There is also a Fortinet section on Nagios exchange:

https://exchange.nagios.org/directory/Plugins/Hardware/Network-Gear/Fortinet

There are no official documentations from Fortinet itself regarding Nagios integration though, only more generic guides to implementing SNMP.