If so, then why would the French permit the Italians to share the intelligence with the British, but permit neither to share the intelligence with the Americans?
Given the behavior of the Chriac regime in France, over the last year or so, that should be self-evident.
There are two (or more) items of intelligence involved. Only one of them was forged. By inserting the forged documents into the pipeline, the French a.) intended that the forgery be discovered, so that b.) it would discredit the other evidence and c.) end up embarrassing the U.S.
The article (and your question) assumes that French intelligence was also the source of the legitimate evidence. That could be the case. But, then again, it may not be. In may be a Frenchman...as distinct from French intelligence.
In any event, we should recognize that, while France is not necessarily an enemy, she is no longer an ally.