I would appreciate it if you could arrange a meeting with Mr. Fukuoka, or introduce me to someone at your company.
Literal
Fukuoka-Mr. [target-に] meet receive-can-[question-か], or your-company [possessive-の] person [object-を] someone introduce receive-can [purpose-よう], request do.
Formal business Japanese (keigo). お会いいただける uses the humble/honorific いただける. ご紹介いただけますよう is a purpose clause with keigo: 'so that you might introduce.' お願いいたします is the humble form of 'I request.'