DIN Next Bold  Suggested by Tomás Silcher 
Coquette  Suggested by frd 

Just in case, here is something similar for "The".

Thanks, and what about the big font?

Now this is a customized logo. Its certainly a DIN, maybe the Bold and slightli italized or maybe just the Vold Italic variant. The "A" has ofc been modified and also added serifs on the "I".
Good luck!