If not, how quickly would news of the invasion have reached northern France?
You may be interested in /u/Yogerthead's answer in the thread, "[Did William the Conqueror know that Harald Hardrada was planning to invade England at the same time?] (https://www.reddit.com/r/AskHistorians/comments/2y0l4l/did_william_the_conqueror_know_that_harald/)"