I was able to solve this using the NTC modules, which use netmiko for SSH connections, which have a handler for FortiGates.
Instructions to install the NTC modules: https://github.com/networktocode/ntc-ansible
Below is sample playbook that shows how to grab the running-config from a FortiGate. Replace the values for host, username, and password. This play does not require an inventory file.
- hosts: localhost
- name: "Gather show-run from FortiGate"