It would appear pdflatex (with [frenchb,english]{babel}) does not do hyphenation of words with an apostrophe.
For example, I wrote "l'arithmétique" which was not hyphened, and the commands \showhyphens{arithmétique} \showhyphens{l'arithmétique} give
ari-thmé-tique and l'arithmétique.
I read the question Hyphenation of words containing apostrophes and while very interesting, I am not inclined to define hyphenation for all words which might be used with apostrophes, especially when another hyphenation might (very, very low chance...) be used elsewhere in the document. I liked the adapted suggestion \newcommand{\?}{'\nobreak\hspace{0pt}} from egreg in the topic, but futhermore I'd like to be able to type an apostrophe to get an apostrophe...
l'arith-mé-tique; are you perhaps using\showhyphensbefore\begin{document}? Or perhaps you don't load\usepackage[T1]{fontenc}? – egreg Jan 02 '15 at 13:40aecompl. – egreg Jan 02 '15 at 13:55