French investigators were trying to determine the provenance of a piece of airplane debris—said by aviation experts to be consistent with the design of the Malaysia Airlines jet that went missing more than a year ago—that washed ashore on an island near Madagascar on Wednesday.

Photos of the debris quickly spread through Boeing’s offices as engineers and mechanics who design and build the company’s widebody jets sought to examine the new clues. Several Boeing employees who reviewed the images separate from the official probe...