فَطَفِقْتُ أَجُوبُ طُرُقَاتِهَا
Then I began to roam its streets.
طَفِقَ belongs to the classical Arabic verbs of inception, indicating that an action has begun. The following present-tense verb أجوب tells us what action is beginning.
طَفِقْتُ — I began.
أَجُوبُ — I roam or traverse.
The compound means “I began to roam,” not merely “I roamed.”