PHP mail() turns text with special characters into attachments

I use the PHP mail() function to send emails to a special interest group.
Some of these mails are in English, no problems, and some of them are in
French. For the latter, the message body text gets turned into an
attachment, and the mail body remains empty. Apparently, it's the
presence of accented characters that triggers this.

The problem appeared when we recently moved the site to a different host.
Both the old and the new host are Linux machines, running PHP 5.4.16 and
Apache 20120211.

Any ideas as to how to prevent my French text from getting hidden away
in an attachment?

Thanks,
Jeroen Belleman