I have not had them enough to know a lot about this. Of 3 roosters last year, I culled one for being a "manfighter." I did breed him one time and saved one male and 3 females from him. The other two cocks are good natured. Of my cockerels this year, I have not had any aggression problems, and they are almost 11 months old. {I know this can be carried by the females too so I expect to see it again but will cull it if I do.}
The breed is flighty especially in a smaller enclosure. I find they are not so "flighty" acting when allowed to free range. They come running to me too. Once caught, they are not crazy & seem to calm down (i.e. they do not wiggle, flap & squirm).
A gentleman who has had the breed a long time told me that his La Fleche males would attack strangers. I have not had this problem with mine.
Historically, I have read quotes from long ago about them not being received well here in USA because they lacked hardiness. However, I have not lost one to sickness & find them hardy and healthy. I know I have Marek's on my premises because in the past, I have lost a Buckeye or two to the disease. Not one of my La Fleche have succumbed so far. I have not vaccinated for anything.
When free ranged, they are prone to going in the deep forest, and I found the remains of two hens in the forest behind my home (out-of- range of the protection of dog and donkey). I have also seen them flying out of the forest almost resembling Guineas in flight. La Fleche fly very well for a chicken.