I live in the Esposende area. There is no easy route from Esposende to Barcelos.
Both roads, either north or south of the river Cávado are fairly busy and in several points don't have much room for pedestrians.
There are tracks used to access the fields and forests by the river which can be used to hike, mostly off-road, up to Barcelos, these are used sometimes by mountain bikers.
Only from the bridge in Fão to the river beach in Fonte Boa (Barca do Lago) is there are straight forward path. Tis is being built to eventually run all the way from the mouth of Cávado River upstream into the Gerês National Park.
Because there are no markings, its a bit of hassle, so I'd recommend taking a bus and using the time to check out the towns.