How can I send a form to a client through email, directly from my website after they made an inquiry

If you want to embed the form in a webpage, here is how:

https://www.jotform.com/help/34-Adding-a-Form-to-a-Web-Page

If you want to send a form via email, please check this guide out:

https://www.jotform.com/help/303-How-to-Send-a-Form-via-Email

But if you want to create an autoresponder.

https://www.jotform.com/help/26-Setting-up-an-Autoresponder-Email