Yes, Forza Horizon 3 includes an offline game mode.
Yes, Forza Horizon 3 offers an offline game mode for PC. It includes all the race events available in the online version.
You can enjoy it offline, though you won’t be able to reach the auction house or use servers such as adventure or freeroam.
You can try the campaign by visiting the provided link and pressing "Ctrl F," then entering "offline."