How do you explain the result for a new \DateTime(‘0000-00-00 00:00:00’)?

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You are seeing two effects here. The first one is that you use a way of writing for a date that can be written in multiple forms:

0000-01-01 same as  0000-01-01
0000-01-00 same as -0001-12-31
0000-00-01 same as -0001-12-01
0000-00-00 same as -0001-11-30

So by the date itself, you already specify the 30th November -1.

Now there’s the time offset left that differs about the 9 minutes and 21 seconds. That is because of a change in the clock compared to UTC in Paris/France that happened 10 Mar 1911 23:51:38/39 local time.

I modified your code example a bit and introduced the Europe/Paris setting as you have it, which is playing a role. This code is telling as well the offset in seconds from UTC (Z) which is what you’re looking for:

$dt = new DateTime('0000-00-00 00:00:00', new DateTimeZone('Europe/Paris'));
printf("%s secs offset from UTC\n", $dt->format('r T (e) Z'));

I changed the dates a bit

Fri, 10 Mar 1911 23:51:38 +0009 PMT (Europe/Paris) 561 secs offset from UTC
                                                   ^^^

One second later:

Fri, 10 Mar 1911 23:51:39 +0000 WET (Europe/Paris) 0 secs offset from UTC

When local standard time was about to reach
Saturday, 11 March 1911, 00:01:00 clocks were turned backward 0:09:21 hours to
Friday, 10 March 1911, 23:51:39 local standard time instead.

That are 561 Secs. Reference: Clock changes in Paris – Time change dates in 1911 and Time zone changes and daylight saving time start/end dates between year 1900 and 1924.

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