Just work through the (free) intro lessons and you will at least learn something that will revolutionize how you think about Thai in your regular classes!
Most people do exactly what you propose (I did too in the beginning) and get nowhere.
No, a "decent teacher" won't help you much, or at least will be very inefficient.
And tell "surrounding yourself with Thai people" to all the expats who have been living here 10 yrs or more and have Thai wives and even children that they still can't communicate with!
Now that you don't need to sit in a class and get nowhere trying to learn Thai just so that you can get an ED visa, why not try a method that really works?
it worked for one of our volunteers applying in London. (Okay so it wasn't a DTV, but the process was the same because they agreed to change the visa type without any additional charge, if the correct documents were submitted. In the end, after considerable toing and froing, they made the amendments to the application manually and issued the correct visa.)
It may be different for Paris, but just send them the updated (correct) info - ie your FULL name exactly as it appears to n your passport - and ask them to reconsider. Other consulates will usually do that. I think it's under "additional uploads" in the evisa system, or you may need to email the consulate directly.