I think the French "vont pointer à l'Assédic/l'ANPE".
Edit: And, of course, muppet that I am, I forgot that, in the context, there are two separate meanings of "to sign on". In the case of signing on every two weeks to claim unemployment benefit, my initial answer stands. On the other hand, if it is the case of the initial signing on to register for unemployment benefit, then I agree with jennycensus and it would be "aller s'inscrire au chômage/à l'Assédic". Ta.