FortiGate Next Generation Firewall utilizes purpose-built security processors and threat intelligence security services from FortiGuard labs to deliver top-rated protection and high performance, including encrypted traffic.
Article Id 195301
This article explains how to download Logs from FortiGate GUI.

Logs can be downloaded from GUI by following  below steps :

After logging in to GUI, go to Log & Report -> click the required log category for example 'System Events' or 'Forward Traffic'
Click on the download icon (on the top of the page).

Log file will be downloaded to “Downloads” folder of the browser.

Note: If a specific lines of log is needed, click on the require log row (for multiple rows press ‘Ctrl’ key on keyboard and then click on the required log row) and then click on download icon.
Also make sure popup blocker or browser download settings are not blocking download.