If you don't want to add any code to the form (as mentioned in the comments to @shadfc's Answer), it is certainly possible, here are two options.
First, you just reference the fields individually in the HTML, rather than the entire form at once:
<form action="" method="post">
<ul class="contactList">
<li id="subject" class="contact">{{ form.subject }}</li>
<li id="email" class="contact">{{ form.email }}</li>
<li id="message" class="contact">{{ form.message }}</li>
</ul>
<input type="submit" value="Submit">
</form>
(Note that I also changed it to a unsorted list.)
Second, note in the docs on outputting forms as HTML, Django:
The Field id, is generated by
prepending 'id_' to the Field name.
The id attributes and tags are
included in the output by default.
All of your form fields already have a unique id. So you would reference id_subject in your CSS file to style the subject field. I should note, this is how the form behaves when you take the default HTML, which requires just printing the form, not the individual fields:
<ul class="contactList">
{{ form }} # Will auto-generate HTML with id_subject, id_email, email_message
{{ form.as_ul }} # might also work, haven't tested
</ul>
See the previous link for other options when outputting forms (you can do tables, etc).
Note - I realize this isn't the same as adding a class to each element (if you added a field to the Form, you'd need to update the CSS also) - but it's easy enough to reference all of the fields by id in your CSS like this:
#id_subject, #id_email, #email_message
{color: red;}