I wanna second his first question.
I have a motobecane conversion that I cannot ride no handed on either. As soon as I take my hands off the bike collapses to the right.
The fork is brand new and the wheels are my old stock pista wheels. Now I could ride flawlessly no handed on my pista with those wheels so I assume they are fine, and the fork is new so that shouldn't be an issue, so is it most likely just the frame?
Any thoughts would be greatly appreciated.