Voici une solution avec l'extension `apptools`, qui définit le test `\IfAppendix` :
\documentclass[a4paper, french]{report}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}%
\usepackage{fourier, erewhon}%
\usepackage[showframe]{geometry}%
\usepackage{babel} \usepackage{titlesec}
\usepackage{apptools}
\titleformat{\chapter}[hang]{\bfseries\huge}{\IfAppendix{\appendixname~}{\relax}\thechapter\IfAppendix{.}{}}{\IfAppendix{0.333em}{2pc}}{}
\renewcommand\chaptername{}
\AtAppendix{\renewcommand\chaptername{\appendixname\,}}
\begin{document}
\chapter{Chapitre premier}
\chapter{Chapitre second}
\appendix
\chapter{Palpitants Détails}
\end{document}
![alt text][1]
![alt text][2]
[1]: http://texnique.fr:80/osqa/upfiles/appendixnameintitlenew1_6SuOnCI.png
[2]: http://texnique.fr:80/osqa/upfiles/appendixnameintitlenew_pruPUrR.png
