Falcon Aviation, Malmö, Sweden, 1983-2006.     -     #2:

Far Eastern Air Transport, logo: FAT, Taipeh, Taiwan, 1957-2008, relaunched 2011-2019:
    -        #4,                                   #2,                                  #8,                                    #1:

Farner Air Transport, Basel, Switzerland, founded 1984,
renamed 1997 to Farnair Europe (logo: FAT).           -    #1:
 
Fars Air Qeshm,  Qeshm, Iran, founded 2006.      -   #2:

Faucett Peru, Lima, 1928-1999.     -   #1A:

FDA Fuji Dream Airlines, Makinohara, Shizuoka, Japan, founded 2009 :

Finnair, Helsinki, founded 1926.
These 3 bags are representing a lot of variations from #1 -14:
 
-    #15,                                #16,                                #17,                                            #18:

-      23:

FINNAVIATION, Helsinki, Finland, 1950 - 1996.       -   #1:

Firefly,  Kuala Lumpur, Malaysia, founded 2007.     -   #1:

First Choice Airways, Manchester, UK,
1987-2002. Merged with ThomsonFly to Thomson Airways:

First Nation Airways, Lagos, Nigeria, founded 2011.   -   #1:

Fischer Air, Praque, Czechia, 1997-2005.    -#1(Logo 4,8cm) / #2(Logo 3,8cm):

FlugServiceBerlin, Berlin, Germany, 1990-1993.  -     #1:

Fly540 (Five Forty Aviation Ltd.), Nairobi, Kenya, founded 2006.    -  #1

FlyBaghdad, Baghdad, Iraq, founded 2915.    -  #1:

flybe. british european, Exeter, UK, founded 1979 as Jersey European,
renamed 2000 to British European and finally 2002 to flybe, ceased 2020.      -    #1:

flyme, Male, Maldives, founded 2011.             -  #1,                         #2,                    #3:

Fly FTI, Munich, Germany, 1999-2001.    -     #1,                        #2,                       #3:

Fly Gangwon,  YangYang, South-Korea, 2019-2023:

Flying Bulls, Salzburg, Austria.  - #1(grey print)/#3(silver print and ELAG at base),      #2:

Flying Colours, UK, 1996-2000, merged to JMC(q.v.).     -  #2:

flyKiss (SiAvia), Ljubljana, Slovenia, founded 2012.  flyKiss is a trademark of SiAvia. In 2016 operating
base Clermont-Ferrand, France, with1 ETR-145 in livery French-look, ceased 2017.    -  #1:

Fly Lili, Bucharest, Romania, *2021.  -  #1:

flyPersia,  Tehran, Iran, *2018.   -   #1:

flysolomons - q.v.:  Solomon Airlines, Papua-New Guinea -    #3:

FMI Air, Yangon, Myanmar, founded 2012.    -  #1(front and rear shown):

Fred. Olsen Airtransport, Oslo-Fornebu, Norway, 1946 - 1997.    -  #1:

FREEBIRD, Istanbul, Turkey, *2001.   Real name: Hürkus Hvayolu Tasimacilik ve Ticaret.   
  -              #1,                  #2,             #4(black print, no maker),    #8(blue print, maker Mojen):

Formosa Airlines, Taiwan, 1987-1999 merged with Mandarin (q.v.).   -#3:

Frenchbee, Paris, France, founded 2018 by renaming from Frenchblue.   - #1:

FRONTIER  the 1st, Denver, Colorado, USA, 1950-1986 merged into Continental(q.v.).  - #2:

FRONTIER  the 2nd, Denver, Colorado, USA,
founded(name revived) 1994 by former staff of Frontier the 1st.      - #7:                
FUTURA, Palma d.M., Spain, 1989 - 2008.
-    #3(all red print),    #6(light green w red logo),                    #1,                           #8:

Fuzhou Airlines, China, founded 2014.        -  #1,                           #2: