Form plugin for pre-built HTML form

I’ve built a custom contact form for a client and am implementing it with his WordPress site. The fields:

Name*
Company
Email*
Phone
Address 1 and 2
City/State/ZIP (state is drop-down menu)
Mode of contact (drop-down)
TOS agreement* (required checkbox)

All the plugins I’ve tried to handle the emailing and validation don’t take premade code and instead build their own forms, which I don’t want.

**Is there a plugin that simply applies validation to the inputs I want and will function as a formmail script?

Thanks in advance,
Jeremy