The issues with water quality in the Seine River in Paris have been reported on extensively. Paris has a combined sewer and storm water system - and spent billions on new treatment plants and storage tanks in an effort to make the water clean enough for the games. Since the Arkansas River in Colorado doesn't have major sewage waste running into the river, it's generally a cleaner river - although it can still contain potentially hazardous bacteria.
But in terms of similarities - these two important rivers are as similar as a balance beam routine is to archery: not very.
The Seine and Arkansas are both considered significant and major rivers for France and the U.S respectively. The Seine is France's third longest river at 485 miles, the Arkansas is the U.S' 6th longest but is actually three times the length of the Seine: 1,470 miles! That's partly a function of the much larger size of the continental United States to France.
Geographically, the Seine starts in eastern France in the Burgundy region. If that name sounds familiar, it's famous for its wine-making. Unlike the Arkansas, the origin of the Seine is not mountain-fed. Its origin, at 1500 ft above sea level, is primarily a drainage for rainfall. The Seine does get some flow from hill drainage and snowmelt but this is due to other tributaries flowing into it along its path, rather than at its start. The Arkansas traces its origins to near Leadville, at 9,750 feet above sea level.
At least in Colorado, bacteria and other microorganism levels are lower in the Arkansas than in the Seine.
Between origin and city - the Seine winds through about 250 miles before reaching Paris, growing in size, speed, and depth as it does. In Paris it averages 5,000-7,000 cubic feet per second (cfs) through the city. That would fill an Olympic sized swimming pool in 12 seconds. The Arkansas flows 150 miles from its source to Pueblo. But these are wildly different paths. The Seine drops about 1,000 vertical feet. The Arkansas...nearly 5,000 feet, particularly leaving the central mountains and contributing to its world-famous rapids as the river charges down through the Royal Gorge. A calm swim it is not!
The modern Seine river in Paris is artificially deep - about 30 feet on average due to a series of downstream locks built during the industrial revolution, and built up edges for the sides of the river. After major storms the river can swell higher with an enhanced flow rate several times its average. That happened this week, contributing to the postponement of the triathlon event (it doesn't help that the combined storm water and sewer system led to E. Coli entering the river).
Meanwhile...as the Arkansas flows through Pueblo...it can during peak-season reach levels of 7-8 feet in parts of the city, but for much of the year and in most spots, it is lower. That's not even half of what's required for Olympic diving. It also doesn't come close in flow rate, averaging 800 to 1000 cfs...about 15 percent of the Seine's flow, at this time of year. At that rate, it'd take about a minute and a half to fill that same pool. It's worth noting that both rivers have annual variation in their flow rates - but the Arkansas river is more dramatic, with flow increasing by a factor of 2-4 during peak snow melt season.
There is one spot of similarity: summer water temperatures. The Seine in Paris, and Arkansas in Pueblo, are both currently sitting near 70 degrees. They can range from around 60-70 degrees Fahrenheit in July.
If you want to find a better comparison for the Arkansas...you'll be in for a long trip. It isn't until the Arkansas approaches its confluence (merge point) with the Mississippi River that its stream flow and general characteristics look similar to the Seine in Paris. In this match up, the city of light has the more Olympics-ready river.
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