Thank you Karl.

The code submitted to fix this issue generates a 'font-size:70' for sup.french, which is obviously quite large…

Escaping the '%' sign fixes this issue:

--- html4.4ht 2014-02-19 14:10:25.634970719 +0100
+++ html4.4ht.new 2014-02-19 14:10:41.518970055 +0100
@@ -30066,7 +30066,7 @@
\Configure{frenchup}{\HCode{<sup class="french">}}{\HCode{</sup>}}
\Css{sup.french{
vertical-align:super;
-font-size:70%;
+font-size:70\%;
}}
\renewcommand\fup[1]{\a:frenchup#1\b:frenchup}

There are two issues with French babel:

1. html entity &nbsp; is inserted before colon. This causes validation error in some xml environments, where this entity is not defined, for example in epub3. macro \:nbsp should be used instead. Patch for the file tex4ht-html4.tex is provided in the attachment.

2. french babel provides some macros which put some text to the superscript. standard macros for superscripts aren't used, so these superscripts doesn't show in the html output. There is a fix for this error:

\NewConfigure{frenchup}{2}
\Configure{frenchup}{\HCode{<sup class="french">}}{\HCode{</sup>}}
\Css{sup.french{
vertical-align:super;
font-size:70%;
}}
\renewcommand\fup[1]{\a:frenchup#1\b:frenchup}

This code should be put to the file tex4ht-4ht.tex, section frenchb.ldf. Unfortunately, I don't really understand structure of tex4ht literate sources and my attemps to process them for generating the output files end with errors, so I posted this only as a code snippet.