A simple google search tells me that "Haggard" emerged in...
...mid 16th century (used in falconry): from French hagard ; perhaps related to hedge; later influenced by hag.
However, on a Discovery Channel program recently, I got to know about Hagar. She was the wife of the patriarch and Islamic prophet Ibrāhīm (Abraham) and the mother of the Ismā'īl (Ishmael).
...was stranded in a desert, and ran between the Al-Safa and Al-Marwah hills in search of water for her son. After the seventh run between the two hills, an angel appeared before her. He helped her and told her that God had heard Ishmael's crying and would provide them with water.
I cannot help but wonder, the english word "haggard" meaning -
"looking exhausted and unwell, especially from fatigue, worry, or suffering."
...could easily have emerged from the story of Hagar as even she must have been exhausted.
Is there any way to be sure?
PS: all information from http://en.wikipedia.org/wiki/Hagar_in_Islam.