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These scenes are completely optional, but once you trigger all of them the two will marry. Raising heart levels and triggering scenes is the only way to get a rival couple married off.
To trigger Julius and Candace's 7 heart event, have 7 hearts with Candace (if you are female), or 7 hearts with Julius (if you are male). Go to the Julius' house during the day after seeing the 4 and 5 heart events. Julius will ask Candace to marry him, and she will accept.