The first part of causeway derives from causey, a word that is not widely used now, meaning (among other things) a causeway.
The ultimate origins of causey appear to be a matter of dispute.
Etymology: Middle English caucé, < Old Northern French (Norman) caucie, earlier cauciée (Picard cauchie < cauchiée, Parisian chauciée occas. chaucie, now chaussée = Provençal caussada, Spanish calzada < late Latin calceāta, calciāta, in Du Cange (who has also via calciata, littus calciatum, cheminus calciatus; probably < a late Latin calciāre ‘to stamp with the heels, to tread’, recorded by Du Cange. The meaning would then be a mound or dam made firm by stamping or treading down.
This is strengthened by the fact that calciāre in medieval Latin interchanges with calcāre to ‘tread, stamp’, and that calcāta, calcātum are actually found instead of calciāta, calciātum; also calcāgium for the droit de chaussée or road-toll. The Romanic forms are (necessarily) identical with those derived < Latin calceāre to shoe (Italian calzare, Spanish calzar, Catalan calsar, Provençal caussar, Old French cauchier, caucier, chaucier, French chausser), whence some have suggested the meaning ‘shod way’, whatever this might be. Diez and others have conjectured a verb of type *calceāre, or *calciāre, < calx, calcem ‘lime’, and taken calceāta as something built or formed with lime; but there is no trace of such a sense in any language. Other medieval Latin forms were calcea mound, high way, paved way, also calceia, calcetum, calceta, all apparently formed on the French. The Old French forms in -ie (from end of 12th cent.), represent earlier ones in -iée; the Anglo-Norman would be caucée, caucé.