CSS - Styling a form - html

Question

I'm styling a form for a site and I need it to look like this -
My coded version, so far, looks like this -
The name & email sections for some reason won't size properly and there seems to be padding or margin properties somewhere which I can't seem to override. Here's my code as it stands -
form {
height: 200px;
width: 400px;
margin-right: 50px;
}
.name {
float: left;
}
input[type=text],
input[type=email] {
background: #F0F0F0;
font-size: 10px;
width: 100%;
height: 20px;
}
input[type=subject] {
background: #F0F0F0;
font-size: 10px;
width: 100%;
height: 20px;
}
textarea {
resize: vertical;
font-size: 10px;
width: 100%;
background: #F0F0F0;
height: 100px;
}
input[type=submit] {
background: #00bfff;
border: none;
color: #ffffff;
cursor: pointer;
font-size: 10px;
font-weight: 700;
width: 100%;
}
<div class="six columns">
<form>
<fieldset>
<div class="name">
<input type="text" required placeholder="NAME">
</div>
<div class="name">
<input type="email" required placeholder="EMAIL">
</div>
<div>
<input type="subject" placeholder="SUBJECT">
</div>
<div>
<textarea placeholder="MESSAGE..."></textarea>
</div>
</fieldset>
<input type="submit" value="SUBMIT">
</form>
</div>
UPDATE - Latest version.

Answer 1

I made a bunch of tweaks and kind of last track as I went, so I hope you're able to read through this and figure it out. If not, please feel free to ask questions!
form {
height: 200px;
width: 400px;
margin-right: 50px;
}
fieldset {
border: none;
padding: 0;
margin: 0;
display: flex;
}
div.row {
display: flex;
width: 100%;
}
div.row input {
margin-left: 5px;
}
div.row input:first-child {
margin-left: 0;
}
input[type=text],
input[type=email] {
background: #E8E8E8;
font-size: 10px;
width: 100%;
box-sizing: border-box;
border: 0;
padding: 0;
margin-bottom: 5px;
padding: 6px 12px;
}
textarea {
resize: none;
font-size: 10px;
background: #E8E8E8;
width: 100%;
box-sizing: border-box;
border: 0;
padding: 6px 12px;
margin-bottom: 5px;
}
input[type=submit] {
background: #1ba4dd;
border: none;
color: #ffffff;
cursor: pointer;
font-size: 10px;
font-weight: 700;
width: 100%;
padding: 8px 0;
}
input[type=submit]:hover {
background: #00bfff;
}
<div class="six columns">
<form>
<fieldset>
<div class="row">
<input name="name" type="text" required placeholder="NAME">
<input name="email" type="email" required placeholder="EMAIL">
</div>
<input name="subject" type="text" placeholder="SUBJECT">
<textarea rows="8" placeholder="MESSAGE..."></textarea>
</fieldset>
<input type="submit" value="SUBMIT">
</form>
</div>