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All right, found the solution after few days, thanks to the following French topic on the same matter back in 2017:

In case this can help others, here is a translation of the fix:

This is a bug from the template "shipping.tpl" (located in theme/templates/checkout/_partials/steps/) 

At the 46th line, the text is <label>{$gift.label}</label> (but this is wrong as it doesn't use the new translation system in the back-office from 1.7 and above).

You need to copy past the following line instead:

<span>{l s='I would like to receive my order in wrapping gift.' d='Shop.Theme.Checkout'}</span>

Then, go back to the back-office and you can find the text translatable.