Well, those are all very "British" ways of using mayonnaise. The French chefs most often avoid using mayonnaise in egg dishes, since it's already an egg-based sauce. Another difference is that in the US/Canada we use mayonnaise mostly as a condiment, while in France it's a sauce, most often a dip, and in some classic salads (not potato salad, that's a British-American dish) like niçoise (tuna, beens, hard-boiled eggs, black olives) or remoulade (mayonnaise, but with extra mustard). Aside from fries, the most classic usage of mayonnaise remains with fish dishes (aioli again, or Tartare sauce, a variant of mayonnaise). Aioli is often served with roasted veggies.

The American industrial type (Kraft and co.) is gross, the liaison/thickening is done by texture agents and thus it doesn't taste much on its own (unless one think of an atrocity like Miracle Whip as mayonnaise!). With fries it's just oily, adds no taste and and is pretty disgusting. To get good mayonnaise here, you have to make it yourself. French/Belgian mayonnaise is not lacking in flavour. One of the basic ingredients is hot French mustard (that's the natural thickener that helps emulsify the sauce and hold it together afterward), so it really doesn't need horseradish (not that the French use that condiment much, it's rather typical of the anglo-saxon cuisines).. Very often, the mayonnaise served with fries is one of the variants of the basic sauce (oil, whole eggs or yolk only, mustard, salt - that's it), such as aioli, a southern French mayonnaise which used grounded roasted garlic, or in some areas the variant using paprika or Espelette pepper. Fries joints usually offer a variety of options.