OK, I'm pushed for time right now - but here's a different suggestion (this is for DF 9.2, if you are really on 8.2 you'll have to guess at the equivalent line numbers, exact line entries, etc):
Add a new line in /language/english/your_account.php at around line 61, or at the end, makes no difference, like so:
define('_REGISTRATIONTEXT','. . . put copied text in here . . . ');
Then in module /modules/Your_Account/register.php on line 45:
<td><span class="genmed"><br />'.$user_cfg['registermsg'].'<br /><br />'._BOUNDREGISTRATION.'<br /><br /></span><div align="center">
change $user_cfg['registermsg'] to _REGISTRATIONTEXT (ie switch it to read from the language file, like the rest of the page, rather than from the db), e.g:
<td><span class="genmed"><br />'._REGISTRATIONTEXT.'<br /><br />'._BOUNDREGISTRATION.'<br /><br /></span><div align="center">
If that works in English, then you should just have to add the same new text line to /language/french/your_account.php, and to every other language translation that you want to support, and it should work.
Sorry I have no time to test this. Please report back if this works for you, as I'm sure others will need it - including me quite possibly in a future project. And post the translations that you have come up with for the benefit of us mono-linguists

?