I noticed that in file wp-content\plugins\freshmail-integration\src\Plugin\Newsletter\Freshmail.php
action wpcf7_before_send_mail (line: 1305) has exit instruction so wpcf7_mail_sent action is not run.
I just comment:
//echo json_encode($ResponcCF7);
//exit;
and for me all is ok.
Script register freshmail subscription if fm-sign input is avaliable in form and send mail using wpcf7.