Does Craft have an equivalent of EE's Custom Fields loop for front-end entry forms?
Personally I don't have any experience with Free Form but have been using Sprout forms for quite some time now.

In Sprout forms your client can create entire forms or just add a couple of fields however you like it. The support on Sprout forms is decent aswell.

Plus sprout forms got email notifications aswell which might be interesting for your client.