The reason why EXM message is not sent in preferred language after form is submitted and "Send email campaign message" action is triggered is quite simple: when contact does that on the website, nothing set preferred language of the contact.
So what happens there? Action is triggered and action creates a contact with values specified in form action editor: 
But you can only specify there email and consent fields.
When action is triggered, Sitecore attempts to retrieve the contact with given identifier from xDB. If it exists in xDB already, mail is sent. If not, new contact is created using exm.sendEmailSubmitAction/createContact pipeline. But the pipeline only sets EmailAddressList and ConsentInformation facets. It does not update contact language.
After the action has the right contact, it creates new EXM dispatch task.
So how can we make sure that contact has preferred language set?
Well, the answer is most probably not what you want to hear: you have to write a code that will do this for you.
The simplest way to achieve that is create a new submit action that will update contact preferred language which is stored in
contact.GetFacet<PersonalInformation>()?.PreferredLanguage
How to do that? There are so many sources for that information that I'm not going to include the code in this answer. I think the best source is official Sitecore documentation:
https://doc.sitecore.com/xp/en/developers/103/sitecore-experience-manager/walkthrough--creating-a-custom-submit-action-that-updates-contact-details.html
You just need to modify it a bit to include setting preferred language. Something like that should do the trick:
using (XConnectClient client = SitecoreXConnectClientConfiguration.GetClient()) { var personalInfo = contact.GetFacet<PersonalInformation>(PersonalInformation.DefaultFacetKey); if (personalInfo == null) { personalInfo = new PersonalInformation(); } // or any other logic to determine preferred language personalInfo.PreferredLanguage = Sitecore.Context.Language.Name; client.SetFacet(contact, PersonalInformation.DefaultFacetKey, personalInfo); client.Submit(); }
