Like Smittie, I don't see Docs as part of a traditionally classic style. However, I do see ways that they could fit into a "CASUAL MODERN classic style".
If you want to stress "classic", an obvious choice would be to team black Docs with black bottoms (pants, jeans, skirts, dresses), or burgunder Docs with burgunder bottoms.
The floral Docs shown by Bijou are fun and could easily be teamed with more classic items, like the stripey blue & white dress (2 of the colours in the shoes) or simply with blue jeans and a white shirt.
Other possibilities:
- black Docs + white jeans + stripey black & white T-shirt or sweater
- white Docs + a breezy skirt or dress (in any colour), for a summer-ish look
- white Docs + black & white checked pants + a black or white sweater, year round
- bottle green Docs + black bottoms + bottle green sweater + maybe chunky white pearls (or just one chunky pearl as a pendant)
All these outfits could be called "casual modern classic" in my book.
Final tip: If you make sure the Docs are polished and well cared for, it will be easier to make them part of a classic style.