AUCTeX can't find file when there is an umlaut in its name (on Mac OS X)

I’m using AUCTeX for Emacs. I’ve got a LaTeX document that compiles fine outside of AUCTeX (so the file itself is fine). However, when I try to compile it from inside Emacs using Ctrl-C Ctrl C, I get the following error:

Running `LaTeX' on `Übungsaufgaben' with ``pdflatex --synctex=1 -interaction=nonstopmode "input" Übungsaufgaben.tex''
This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013)
 restricted write18 enabled.
entering extended mode
LaTeX2e <2011/06/27>
Babel <3.9f> and hyphenation patterns for 78 languages loaded.
! I can't find file `Übungsaufgaben.tex'.
<*> input Übungsaufgaben.tex

(Press Enter to retry, or Control-D to exit)
Please type another input file name
! Emergency stop.
<*> input Übungsaufgaben.tex

!  ==> Fatal error occurred, no output PDF file produced!
Transcript written on texput.log.

LaTeX exited abnormally with code 1 at Mon Jun  2 15:09:56

Replacing the Ü in the filename with “Ue” it works fine so the non ASCII character in the file name appears to be a problem.

Compiling from the terminal also works. locale gives me:

LANG="de_DE.UTF-8"
LC_COLLATE="de_DE.UTF-8"
LC_CTYPE="de_DE.UTF-8"
LC_MESSAGES="de_DE.UTF-8"
LC_MONETARY="de_DE.UTF-8"
LC_NUMERIC="de_DE.UTF-8"
LC_TIME="de_DE.UTF-8"
LC_ALL=

I’m using Aquamacs on OS X 10.9.3. I installed TeX Live via MacTeX and have not modified anything (vanilla LaTeX, “vanilla” Aquamacs, “vanilla” AUCTeX that comes with Aquamacs).

I’m not sure what the actual problem is (it should find the file) or how to fix it so any help would be much appreciated!

(set-language-environment 'utf-8)
(set-language-environment "UTF-8")
(setq default-file-name-coding-system 'iso-8859-15)
(setq default-file-name-coding-system 'utf-8-dos)
(setq file-name-coding-system 'utf-8)