Time::Local gives the first day of the month:

use Time::Local;

my $time = timelocal(0,0,0,1,7,2003);

my $day .= localtime($time);

print $day, "\n";
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which outputs:

Fri Aug  1 00:00:00 2003
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Note that the days number from 1, but months number from 0.

Using the list output of localtime would give you a day of the week numeral that you could use to calculate the first Monday.

--Bob Niederman, http://bob-n.com