Are these terms interchangeable?
Freeform Writing Exercise A2
which is more of a random event, unsuitable here.
Yes and no. Sometimes they can be interchangeable, other times their difference matters.
Heureusement refers more to the happy side of lucky, whereas par chance is about the chancy side of lucky.
I suggest you look them both up in one of the many online dictionaries which can give you a broader perspective.
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