Which fruit compounds affect the speed of fructose absorption?
Yes they do. The answer is glucose.

Let's begin at the beginning: you eat a piece of fruit. The fruit contains many different kinds of sugars, including fructose and glucose. One of the immediate effects your digestion of this fruit has is to raise the levels in your blood of every type of sugar that was present, and the blood levels of many other types of nutrients as well. This has nothing to do with how well your body does/doesn't absorb fructose, it is simply a normal step in digestion.

Next, GLUT2 transporters in the insulin producing cells in your pancreas import glucose. This acts as a signal that tells those cells to start producing insulin. Insulin then diffuses around the body and produces myriad effects, including upregulation of GLUT4  activity across the body. These GLUT4 transporters are present on cells in many parts of your body and are what are responsible for taking up most of the glucose from your blood.

Now on to fructose. GLUT5 is the main fructose transporter. Just like GLUT4, GLUT5 activity is also regulated by insulin, but in a less quick and dramatic fashion than with GLUT4. Although there's a large body of work showing that GLUT5 does not respond quickly to insulin, recent work has shown that, for example, high levels of insulin lead to increased GLUT5 activity in skeletal muscle over a period of 24 hours.

So if what your trying to get at is some reason why eating an apple is better for you than chugging an equivalent volume of Auntie Jemimah's pure corn syrup, it's always going to be some reason like this where you have co-metabolism of several nutrients that tend to show up together in "natural" food. It is unlikely that there are any complex plant substances that would be primarily responsible for the health benefit of fresh fruit in general.