You first took a French class at the end of the five years. I had been living ... is appropriate.
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sb70012I (1) was living in Paris (2) for five years ...Parts (1) and (2) of this clause are inconsistent. (1) indicates an open time period, i.e., a period with no definite beginning or end, hence with no define duration. (2) indicates a closed time period; it specifies a duration.