I agree that the revised French editions of Taghon's books are well worth getting in addition to the German originals. The first one was published in 2017 and the second one is due very soon.
As Stukapilot said, there are no English books on LG 1, but there is another German one:
"Die Ritterkreuzträger des LG 1, 1939-1945" by Ralf Schumann, VDM Heinz Nickel, 2007, 220 pages, ISBN: 978-3-86619-013-9
It contains:
- a short history of the unit (5 pages)
- a profile of each RKT (a few pages each + photos)
- a list of all unit members awarded the Deutschen Kreuz in Gold
- a list of all unit members awarded the Ehrenpokal
- a list of the unit's Kommodore
- a list of all Luftwaffe generals who served in the unit
- a list of the unit's personnel losses
- unit OOBs for various dates
- Feldpostnummern for the Stab and each Gruppe
- pictures of the Geschwader and Gruppe emblems
- a list of Verbandskennzeichnungen for all Kampfgeschwader units
FYI, Schumann also did similar volumes on KG 1 and KG 2.
Hope that helps,
Leon Venter