Using Monit 5.16 (stock package Ubuntu 16.04), this configuration:
Process Name = php7.1-fpm
Pid file = /var/run/php/php7.1-fpm.pid
Monitoring mode = active
Start program = '/usr/sbin/service php7.1-fpm start' timeout 30 second(s)
Stop program = '/usr/sbin/service php7.1-fpm stop' timeout 30 second(s)
Restart program = '/usr/sbin/service php7.1-fpm restart' timeout 30 second(s)
Existence = if does not exist then restart