You are already capturing it in $2. You just need to print it:

use warnings;
use strict;

my $str = "This is a string which has bi-weekly data";
if ($str =~ /(\w+)[- ](daily|month|days|weekly|week)/) {
    my $found= $1;                    
    print "$found $2\n";
} 

__END__

bi weekly
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