Timezone issue with cron

(Copying my comment as an answer, since it turned out to be the solution; I guessed right.)

So cron jobs are being scheduled in UTC (Europe/Paris is at a one hour offset from UTC).

The Vixie cron man page says:

The daemon will use, if present, the definition from /etc/timezone for the timezone.

What's in /etc/timezone? Have you modified /etc/timezone more recently than the cron process was started? Have you tried

/etc/init.d/cron restart

?

Some distros such as Fedora provide a mechanism where you can set CRON_TZ= to override your default timezone.

From the Fedora man 5 crontab

The CRON_TZ variable specifies the time zone specific for the cron table. The user should enter a time according to the specified time zone into the table. The time used for writing into a log file is taken from the local time zone, where the daemon is running.

Something like this:

#m  h           d   m   wday    command
CRON_TZ="Europe/Paris"
5   0,6,12,18   *   *   *       /path/to/script.bash