For situations where you have a stream of lines, a here-doc can significantly improve readability. As well, a two-argument open without a check is considered bad practice. Combining all this with a lexical filehandle and poj's suggestion, I might write your script as:

my $emailTo = 'Customer Service <customerservice@df-foods.com>';
my $emailCC = 'Frank Simmons <fsimmons@oregonpotato.com,susan@ftiegs.c
+om,jenbrink@icloud.com>';
my $emailFrom = FilterCChars($FTGEmail);

open(my $mail,'|-', $mailProg) or die "Problem accessing $mailProg: $!
+";

print $mail <<EOT;
To: $emailTo
Cc: $emailCC
From: $emailFrom
Subject: $emailSubject
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: 8bit

$emailBody
EOT
close $mail;

# Redirect user to success page

print "Location: /thankyou.html\n\n";

exit;
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Note how much cleaner that looks without all the newlines and print commands.