Entrenches rhymes with:
trenches, french's, trenches, wrenches, benches, french's, trenches, wenches, wrenches, avalanches, benches, branch's, brunches, bulfinch's, crunches, finches, french's, funches, goldfinches, hunches, lunches, lynch's, punches, ranch's, trenches, wenches, wrenches
Entrenches sounds like:
endearing, endothermic, endotronics, endotronics', endotronics's, endurance, enduring, entering, entrance, entrances, entrench