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French professional emails have one register: formal. Veuillez agréer l'expression de mes sentiments distingués is standard. English doesn't work that way. Using ultra-formal English in a casual workplace sounds robotic. Using casual English with a new client sounds unprofessional.
First email = match their level. If they wrote "Hi," don't reply with "Dear." Match, then gradually adjust.
"Please find enclosed herewith the document pertaining to our discussion" — say "Here's the document we discussed." Also: "Dear Sir or Madam" when you know their name. Use it: "Dear Ms. Chen," or "Hi Ms. Chen,"