You cannot set the font to be used in form fields in InDesign. Apparently the default font does not have the extended characters you need.
That will have to be corrected in Acrobat Pro.
In this thread Re: Which charactersets are supported by interactive pdf created in ID? (Norwegians ÆØÅ missing) Willi Adelberger says that this was a bug that was fixed in an update to InDesign CS6.
So, if you've got CS6, make sure you're fully patched. If you don't and this issue is important for you, you should upgrade.
Interesting. Missed that.
Thank you so much Ariel! It works fine now