Merci pour l'invitation, mais je ne pourrai pas venir.
to send an invitation is 'envoyer une invitation' in French.
l'invitation
Say thankyou for the invite, but then say that you don't really feel like attending.
refuse his invitation
They tend to tell a white lie and say that they have something else on at the date or time.
Nope... but what invitation are you talking about?
merci madame or monsieur
playwrights
The French word for "invitation" is (drum roll, please): "invitation."
Une invitation d'anniversaire (literally "an invitation of birthday").
I ruefully had to refuse the invitation as I had a prior appointment
To refuse an appointment, be polite and respectful in your communication. Express your gratitude for the invitation, give a brief reason for your inability to attend, and offer to reschedule if possible. Clarify your decision clearly and professionally to maintain good relations.