Both words go back to French, and from French back to Latin.
Channel is the older word and represents the ordinary phonological development from Latin canalis to Old French - compare Latin canis and French chien. Its primary sense, then as now, was the ‘bed’ in which water runs: a river, or larger body such as the English Channel. From that the word was extended to tubes and pipes and gutters in which water runs, and to similarly formed grooves, and eventually to metaphoric uses such as ‘diplomatic’ ‘channels of communication’. This last use is the origin of channel for specific frequencies of broadcast signal.
The French ‘readopted’ the Latin word in the 16th century as canal for various scientific and technological uses, and English ‘reborrowed’ it for the same purposes; this was the beginning of the age of international scientific discourse, and French was then the leading language for that purpose. One of the new uses was for an artificial watercourse; and when canals began to be dug as great public projects, it became in English the primary sense of that word.