What law did saint valentine break?

Nobody knows. We don't even know who Valentinus really was or where he lived. The popular legends about him all started well (like, a thousand years) after his death and appear to be almost entirely fictional. The pope who established his feast day (about a hundred years after his death) said only that his name was "justly reverenced among men" but that his "acts were known only to God"... in other Words, even HE didn't know exactly what Valentinus had done, just that he was a martyr for Christ.