If the nations occupying these canal networks have cannons, there isn't going to BE any naval combat.
Not anywhere within range of land-based artillery at any rate. It's always cheaper and easier to put your cannons in a fortification than on a boat, and you can put MUCH larger cannons in a fortification more easily than you can on a boat. The advantage of warships, in a fifteenth/sixteenth century technological setting is that they can go anywhere there's water, but in your setting that advantage is reversed. The canals provide a massive advantage to defenders in any kind of military engagement. Mobility offers no advantage if you can't use it to move past your opponent without engaging him, and canals make that impossible.
The only time you might have ship-on-ship combat would be out in the middle of nowhere, in areas where neither side has fortifications or cities. Even here, the most effective tool would be the biggest, slowest, most heavily armed floating platforms you can build. Even then, you couldn't bring something like that in range of an enemy ground emplacement without assaulting it on LAND first and disabling its guns.
Your civilizations might have had extensive naval battles at a technology level equivalent to the first or second century, when weapons didn't really exist that could disable ships from 3-400 yards away. You might have had great naval engagements on par with the Battle of Salamis where the Greeks beat the Persians
The moment someone invented even a really good trebuchet though, it would spark a spectacular arms race towards massive defensive artillery, and nothing that floats could get anywhere close without their permission. That means that wars between these nations would primarily be conducted with CAVALRY, not ships, operating out in the open areas in between canals and cities, raiding smaller towns and burning crops and so forth. The only way to take a defended city would be by seiging it and cutting off it's food supply first, and you can't do that with ships in this scenario.
The main use I see for ships in this setting is as cargo vessels. You'd us them to move your troops long distances more quickly than they could march, but you'd disembark them for actual combat. Other than that you might have fast galleys being used as scouts and maybe commerce raiders, and they'd get in 2 and 3 ship squabbles sometimes, but they'd be useless for actual large scale warfare between nations.