YOu can not directly put your form value to the URL, SImple way is to submit your form using GET method.
Look at into following code and see what you understand and what you need, modify code accordingly. (click the button, and see the URL)
<form action="index.php" target="_blank" method="get">
<input name="parrinName" type="text"/>
<input type="hidden" name="page" value="impression/lettre_carte_cadeau" />
<input type="hidden" name="output" value="pdf" />
<input type="hidden" name="id" value="2" />
<button name="print" type="submit">
<img src="<?=IMAGES_URL?>fleche.jpg" border="0" align="middle"> Imprimer lettre carte cadeau</a>
</button>
</form>
<?php
//TO get the form values
$name = $_GET['parrinName'];
$id = $_GET['id'];
$page = $_GET['page'];
//..................
//...................
//DO what ever you like
?>
When you press the button, you will get URL like this,
index.php?parrinName=&page=impression%2Flettre_carte_cadeau&output=pdf&id=2&print=
But Remember make hidden those field which you dont want to show and also proper server side validation.