Yes, it is possible to reset the progress and / or restart the game.
Creating a new world
Most of the different language versions in Forge of Empires have more than one world. You can play with the same account on multiple worlds of one language version. If you create a new world, then you will always start at the beginning in Stone Age.
In order to create a new world, you need to log out from your current game via the logout button on the upper right corner:
You will then directed to the main page again. Click on 'Play' and a window will pop up with the world selection. On top you will see the world you're currently playing on.
Underneath another world is recommended to you. If you want to play on a specific world, then go on 'Play in a new world that you haven't discovered yet'. Select the world you want, and start right away at the very beginning.
Delete your own world
If you want to have a fresh start on the same world, then you can also delete it yourself. Go to the settings and open the tab 'Profile', then go to 'Delete City':
You will need to confirm the deletion with you password. The world will be deleted after 14 days. You can cancel the deletion anytime, if you log into the world again. If you have a guest- or Facebook account, you may need to contact our support in order to delete the world.