Forza Motorsport requires an online connection. With that said, you can still play the racing simulator when the game servers or your internet goes down. To see what the offline limitations are for the game, you can take a look at this article from Seeking Tech.
What happens when you try to Forza Motorsport offline?
If you try to play this racing simulator without connecting to its server, you will end up getting the following message:
Not Connected
Progress cannot be saved until connection is restored. You can try to reconnect now or try to play Free Play offline.
Reason: Failed to log on to Forza Game Servers.
So, as stated above, you can only play the Free Play mode, which allows you to race through all the tracks in the game with any car. Of course, you will also be able to use the Settings menu.
Every other option in the home menu will be greyed out, however, if you are connected to the server. You will see a message saying that an “online connection is required.”
It is also important to note that your progress won’t be saved in Free Play mode if you aren’t connected to the online servers. This is done in order to prevent any potential cheating when it comes to earning in-game rewards.
What happens when you re-connect?
If you re-connect to the online servers, you should see the following message pop up:
Connection Restored
Would you like to restart with your last saved online profile?
If you choose to restart, then the game will reboot and be connected to the internet. This will unlock all the other modes in addition to allowing you to save your future progress.