This is a mess:
<td><a class="btn"><button type="submit">Se Connecter</button></a></td>
because you are taking a button and then inside of a table cell but you are then wrapping a link around the button. From HTML point of view (that's what's in control of the actions) you've given the same rendered object to jobs to do concurrently - and it will pick one, probably the out like element, as the live one.
is for how a link behaves (I cause them to "light up" in red, on hover. An element will simply ignore attributes that do not apply to it.
I cannot see the rest of your code, but an input button of type="submit" is only useful in a <form> a button element only does something if you give it an event, almost always onclick=
You need to reorganize in your head what you want the button to do and check into how the HTML works (for actions) and CSS (for :hoover).