Your problem is that you are reading the file line by line but expect three lines in your search pattern

There are a lot of ways you could do this, one would be to use a state machine. It uses a variable that notes which state it is in and depending on the next line switches to an appropriate state.

In this case state 1 means "I'm at the line after the first line I'm looking for" and state 2 means "I'm after the second line which followed the first line, expecting the number now"

#!/usr/bin/perl

use strict;
use warnings;

my @array=();

open (INF, "$file");
my $state= 0;
while (<INF>){
    if ($state==0) {
        if (/^First line of text$/) {
            $state=1;    
        }
        next;
    }

    if ($state==1) {
        if (/^second line of text$/) {
            $state=2;
    }
    elsif (/^First line of text$/) { 
        $state=1; 
    }
    else {
        $state=0;
        }
        next;
    }    

    if ($state==2) {
        if (/^in the third line I have (\d*\.\d*)/) {
            push(@array,$1);
        $state=0;
        }
        elsif (/^First line of text$/) { 
            $state=1; 
        }
        else {
            $state=0;
        }
        next;
    }
}
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Note I used ^ and $ to denote line begin and end in the patterns so that the full lines must correspond to the pattern, not only a part of a line. Also used strict and warnings.