I am afraid that ‘broke with him’ doesn’t quite work. We use the expression ‘break with’ to suggest that you no longer follow for example a tradition or a custom. After years of celebrating the festival in May, the villagers decided to break with tradition and hold it instead in June. The nearest expression to yours would be : She broke up with him.
You may be interested in a piece I’ve written using ‘break’ with different prepositions.