Were Abū Ḥanīfa and Charlemagne alive at the same time?
Yes. Abū Ḥanīfa and Charlemagne were alive at the same time, from AD 740–748 to AD 766–767.
Abū Ḥanīfa
8th-century Sunni theologian and jurist
Born 5 September AD 699 · died AD 766–767, aged 67 or 68
Charlemagne
King of Franks, regarded as the first Holy Roman Emperor (747–814)
Born AD 740–748 · died 28 January AD 814