Making a Smart CTA button display based on page language rather than user's browser language

You can obtain the current page language tag via:

content.language.languageTag

This will output something like ‘en’, ‘en-us’, ‘de’, ‘fr’, etc.

To make a conditional for it, you simply need to put it in an if statement like so:

{% if content.language.languageTag == 'en' %}
 {% cta guid="{{ module.en_cta_field }}" %}
{% elif content.language.languageTag == 'fr' %}
 {% cta guid="{{ module.fr_cta_field }}" %}
{% endif %}

So in your module, you just need to create the corresponding CTAs for each language and make conditionals for it to show on the right pages.