Ironically, independent is apparently spelled that way because the English couldn't (or wouldn't) spell the French "indépendant" correctly.
To get back to the point, communicating means conveying meaning to another. If you do not play by the grammatical rules, you lessen the probability of your meaning getting across, because they are a standard that all parties implicitely decide to use. English has comparatively few grammatical rules, but I can assure you that errors in French can easily alter and degrade understanding. Also, if you put the strain of trying to understand you on others, you are just wasting their time because you did not want to spare yours. Others recognize it and a less liable to repeat the effort.