You should be able to specify one for each language.
If you wanted to do it with code, you can use this example to switch between languages:
<?php if(ICL_LANGUAGE_CODE=='gb'): ?>
<img src="your_logo.jpg"/>
<?php elseif(ICL_LANGUAGE_CODE=='fr'): ?>
<img src="your_logo.jpg"/>
<?php endif;?>
This would require you to have your child theme active and a bit of PHP knowledge to amend the correct function for the logo output. The function is called sf_logo()
and is located here: swift-framework/core/sf-header.php