There’s nice running along the Saône, the river adjacent to Old Lyon. It’s possible to run on both sides, with numerous bridges for crossing — especially in the Old Lyon section. It’s ~8 km between the Confluences (confluence of the two rivers) in the north to Pont Robert Schuman in the south.
East Bank: On the Presqu’île (East) side, it’s a series of dedicated pedestrian paths, bike paths, and shoulder on the road, which can be busy in sections. But there are water views the whole way, and nice views over to Vieux Lyon in the central sections. From Pont Bonaparte headed north (toward Croix-Russe), there’s a section of path below the road along the river for ~2 km. There are several pedestrian bridges (Passarelle) for crossing.
West Bank. It’s also possible to run on the western banks of the Saône, with similar types of paths and roughly similar distances. North of Passerelle St. Georges (pedestrian bridge), there isn’t much of a sidewalk/shoulder, thought the road is fairly quiet.
Add-Ons: Can combine with paths along the Rhone, which is only 0.5 km east in central Lyon. Additional paths in the Confluence area.