I want to write about a city in environments like the grasslands in France. Its progress from its rise until its fall. Could the city expand to an empire in one or two generations? (Middle ages technology level)
So technically it probably could in the right conditions. History has proven that civilizations near rivers and specific resources last longer. But if you want this empire to expand within a few generations it needs to be placed correctly, be lead by a brilliant strategist that can conquer land quickly, and have a large number of grown men and women that have militaristic training and have battle experience.
I would suggest researching old world powers such as the Inca, Indus Valley civilization, Egyptians, Roman Empire, and even Colonial America. They all have specific failings and successes that may help you build the correct setting for your empire to exist.
I believe history of numerous Hansa cities, Venice, Genoa their rise to power and fall will give you all information needed and loot of ideas.
Other part is that 2 generations is not enough 1) Nowadays it's 50 years in middle ages it would be about 30 years - Charlemagne need 50 years to create his empire and he started with huge developed country 2) You can travel alone by horse through France in about 8 days. It would take you months to do it with army 3) During WW2 Germans won in 1 month but it took 9 month to be reclaimed by Allies.
I would rethink time restriction.