This actually pretty hard to do. Here's why: Water flows downstream. You need a difference in water level between upstream and downstream of your city. Flow through a pipe is essentially a rather complicated function - typically you use the Darcy Weissbach equation in combination with a Moody chart - of this level difference. Approximately, the head loss, or required level difference between upstream and downstream, quadruples when you double the flowrate.
In open flows like rivers the relationship is far more complicated because with higher flow rate the river bed or channel is usually filled more, which means less then quadruple head loss for double flow rate. Open channel flow is not trivial but please read around a bit
What does this mean for your city?
Let's take one of the rivers from Kingledions answer, the Seine with low flow around 100 m³/s, average flow of 280 m³/s and extreme flow of 1280 m³/s
It's often a good idea to look at flow systems starting downstream. Let's say at average flow conditions you have a downstream water level of 50m above sea level. You city is 5 km across, really small. This calculator tells me, with an 8m diameter, 5km long pipe, my pressure loss is 72.445 Pa wich is equivalent to a head loss of 7.2 m. So my upstream reservoir level will be 57.2 m at average conditions.
Now, let's take the extreme flow, now I have 1513.962 Pa - 15m! We need a dike between our upstream reservoir that's 65m above sea level, and 7 m above the normal level of the lake or what have you. Actually more, because at extreme flows the downstream level will be higher too, by a few m!
I suggest a second channel or even third that's only opened at high flow events, also play around with the sizing of the pipes.
On the other hand, what happens at low flow? At normal flow, we have a flow velocity of 3.6 m/s . At low flow - 100 m³/s - the flow velocity is 1.3 m/s. The DWA-M 275 (An industrial code, Germany, for designing piping systems in wastewater treatemtn plants that I happebn to have open at the moment) advises a flow velocity of at least 2m/s for raw sewage. Why? Sedimentation! at lower flow velocities, sand etc. will sediment and remain in the pipe. In actuality I don't see this problem, because in all likelyhood your pipe will be the fastest streaming part of the river system.
Environmental impact assessment
The pipe will stop migrating fish, at least most of the time, from swimming upstream. This could seriously impact aquatic ecosystems along your river.