Craft plugin for input fields on the front end to check existing user
If you are creating these as actual users in Craft, it should be possible to do it straight from the template without the need for a plugin, as long as you have Craft PRO (without PRO you anyways wouldn't be able to create more than one "admin" user, and one "client" user anyways):

See the documentation here:
https://craftcms.com/docs/templating/craft.users#email

Basically, you should be able to call craft.users.email('your.email@address.com') to check if it exists. Again, I haven't tested this myself, but it will then return the user if it exists, and otherwise I assume it will return null.