Appropriate is used to describe something that is suitable or proper for a particular situation. For example, “It is appropriate to be on time for an interview.” Apropos is used to describe something that is relevant or appropriate to the current situation. For example, “This topic is apropos for the discussion.”

Apropos means of an appropriate or pertinent nature, not quite by the way or incidental. "Our meeting was apropos, you couldn't have expected a much different reaction." Appropriate means suitable to the social situation, respect, discreetness in accordance to the available norms or customs. "Suits are appropriate for a dinner party."

Apropos Fitting and to the point. Appropriate Suitable for a particular person, condition, occasion, or place; fitting.

The adjectival use of apropos is the least common of the three. I’ve seen forum comments asserting that apropos is “never a synonym for appropriate.” A French borrowing, apropos functions more often as a preposition or as an adverb. Apropos comes from French à propos, “with regard to this purpose.” As an adjective, it is a synonym for appropriate: