Superior methods exist for what you want to do (see other posts and the caveat at the end of this one), but the fix for what you have is simple. You need perl to consider your $input as a string to get it to interpolate. This code should work for you:

use strict;

my $v1="user_value1";

open(INFILE,"<template.file") or die "Couldn't open file: $!";
my $input=<INFILE>;
close(INFILE);

$input = '"' . $input . '"';;

my $line = eval $input;

print "$line\n";
[download]

Depending on your desired output, you might also want to chomp off the newline that comes with $input

Also, be exceedingly careful with how you use this. You typically shouldn't eval anything passed from the user, as you're possibly introducing an enormous security headache. String eval on user data is frequently an open invitation for the user to execute code of their choice. I'd sleep easier at night using the s/// operator to fill in the values if that's an option. If you can't do that for whatever reason, use taint checking and thoroughly consider how your script could be abused.