Why were words for the four cardinal directions (east, west, north, south) in Romance languages borrowed from Old English? They could have used their own words derived from Latin because these words seem to belong to the basic vocabulary, and if anything, the Saxons wouldn't have been the dominant force over the French-speaking authorities (Normans/French).
The French words for the cardinal points (nord, sud, est, ouest) are definitely borrowed from some Germanic language, presumably in connection with seafaring in the North Sea. (This answers the "why" part of your question). The supposition that they were borrowed specifically from Old English (and not, for example, from the Normans) is supported by the observation that French est has an /e/ vowel, like English and Frisian, while all the other Germanic languages have /o/ or /u/. The vowel in English “east” is explained by the assumption of a contamination with suffixed words like “easter”, with Germanic umlaut.
From a phonological point of view, nord, sud, ouest could theoretically derive from Nordic or any other Germanic language, but there is an argument for thinking that all four terms were borrowed from a common source all at the same time.
The forms in other Romance languages are borrowed from French.
Reference: Oxford English Dictionary articles “east” and “easter”.