Standard reduction potentials:
Li+ + e- <--> Li; E0 = -3.02V
Na+ + e- <--> Na; E0 = -2.71V
K+ + e- <--> K; E0 = -2.92V
Rb+ + e- <--> Rb; E0 = -2.92V
Cs+ + e- <--> Cs; E0 = -2.92V
Fr+ + e- <--> Fr; E0 =estimated -2.92V
Francium is very radioactive, and I do not know of anyone who isolated the stable element yet.
The difference is small, but indeed present. Lithium oxidises slightly easier than any of the larger alkali metals.
One of the reasons (likely) in watery solutions is the higher hydration energy of Lithium (hydration energy increases with smaller atomic radius).
now if you are talking in ionization energies (releasing an electron in vacuum), then lithium has a far higher ionization energy due to its smaller radius. I do not know francium's Ei (radioactive), but assume it would be much lower than Li (see for example Li Ei = 520 kJ/mol; Cs Ei = 376 kJ/mol), thus in vacuum I would expect your reasoning to be true and Litium to lose its valence electron less easily.