Looking at the LaTeX file, I see that in the \documentclass command, french and english are listed, with french last. Later, there is a \usepackage{babel}.
However, I cannot find any documentation on using languages as options to \documentclass like this. The rule for using them with \usepackage{babel} is to list the "base" language last, i.e. for me
\usepackage[english,french]{babel}
If I use this command and remove the languages from the \documentclass command, I get the output as expected with the headings in French (when running latex manually, of course).
It looks as though something is wrong in LyX here...but I'm a bit surprised because it seems so obvious.
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