I know this was asked 3 months ago but I think I’ve just found a solution for those who may be still looking. I’m not an expert in CSS but it works for me.
Wrap the form in a div id for example in your Contact Form 7 panel.
<div id = "myform1">
<p>Your Name (required)<br />
[text* your-name] </p>
<p>Your Email (required)<br />
[email* your-email] </p>
<p>Subject<br />
[text your-subject] </p>
<p>Your Message<br />
[textarea your-message] </p>
<p>[submit "Send"]</p>
</div>
Then in your styles.css file
refer to your form using #
#myform1{
background: #F7F7F7;
width : 230px;
margin: 10px auto;
position: relative;
height: 275px;
border: 2px solid #D4F4FF;
border-radius:10px;
-moz-border-radius:10px;
box-shadow: 10px 10px 5px #888888;
}