I was hoping that a key combo such as the Shift+Enter would work but it didn't. You could have them separate the paragraphs with three spaces (or a combo that wouldn't be found in natural type) and then do a replace in the string and replace with /n or /n/n, depending on what spacing you want.
intext = arcpy.GetParameterAsText(0)
if not intext or intext == '':
intext = 'sdffewafaewfwaefawefaewa awefaewfawe afewaewf aewfewafaefa aewfaewfa afwefaefae awefrerafafcaewcew awefewafacawewsfdaesfea'
intext_updated = intext.replace(' ', '\n\n')
...
If you truly want a TextBox, think you'll have to go to the Pro SDK and create an Addin to get access to the WPF controls.