Languages

So, the Demo site, https://demo.moodle.net/, using Boost, also appears to have the same display in that a language dropdown doesn't show on the login page.

As you're only dealing with two language options, you could think about a workaround by adding two links to the text of the page.

These could be either down in the instructions which appear below the heading 'Is this your first time here? as mentioned by Helen in https://moodle.org/mod/forum/discuss.php?d=355178. If using this solution, you'd also need to enclose each link name in multilingual tags (and have the multilingual filter enabled too https://docs.moodle.org/33/en/Multi-language_content_filter)
<span class="multilang" lang="en">English</span>
<span class="multilang" lang="fr">Englais</span>

Otherwise, you could customise your "Forgotten your username or password" string or french equivalent, to display it on the top right of the page, as follows.

Site administration > Language > Language customisation, in the English en pack, it's Component core, String forgotten, "Forgotten your username or password?" and edit it to this instead.

<h3></a><a href="/login/index.php?lang=en">English</a> | <a href="/login/index.php?lang=fr">French</a></h3>
<a href="/login/forgotpassword.php">Forgotten your username or password?

Change the css as required, and of course you would also need to add the same to the French fr pack string too.