I think we have to remember we are talking about additives here and not the supplements themselves.

I don't think we can translate by "additive" either, because the meaning of "additive" and "additif" from the GDT is:
additive
additif n. m.
Définition :
An inert material used in addition to the active or therapeutic ingredient in view to produce a drug.
Note(s) :
Additives may be classified into two groups, according to the part they play in the finished drug. The first group includes diluents, binders and lubricants. The second group includes disintegrators, colors, flavors and sweetening agents.

Personally, I think that they mean that nutritional ingredients were added to the food supplements, and I would probably translate by:
"added nutritional ingredients"

I don't like complementary much but the nutrient additive bit is solid. Nutritional supplements containing complementary nutrient additives... There are lots of "additive-free" nutritional supplements so your text seems to be about all the other ones that do contian additives.

I actually liked the answers with supplements in them, but reading all the comments and arguments...this would be one way to phrase it.