Black walnut secretes a substance named juglone which is toxic to many plants and trees. It is a natural substance that developed to reduce competition from other plants. It mainly occurs as leaves and branches decay, so if you reduce the number of leaves and such under the tree, it shouldn't affect the vines that far away very much. The roots however also contain the substance and can affect the vines if they grow within a few feet of the vine. Below is a partial list of plants found growing under black walnuts, and grapes isn't on it. It would be safest to keep the vines away from the black walnut.
Herbaceous Perennials:
Ajuga reptans; bugleweed
Alcea rosea; hollyhock
Anemone quinquefolia; American Wood Anemone (Ohio)
Arisaema triphyllum; Jack-in-the-Pulpit (Ohio)
Asarum europaeum; European wild ginger
Astilbe
Campanula latifolia; bellflower
Celastrus; Bittersweet (Abraham)
Chrysanthemum; hardy chrysanthemum
Dicentra; Bleeding heart (Abraham)
Digitalis; Foxglove (Abraham)
Doronicum; leopard's bane
Dryopteris cristata; crested wood fern
Galium odoratum; sweet woodruff
Geranium robertianum; herb Robert
Geranium sanguineum; cranesbill
Gramineae family; Grasses (most- Ohio) ( many- Abraham)
Helianthus tuberosus; Jerusalem artichoke
Hemerocallis- daylilies- (Abraham)
Heuchera xbrizoides; 'Pluie de Feu', coral bells
Hieracium aurantiacum; orange hawkweed
Hosta- general (Abraham)
Hosta forunei; 'Glauca', plantrain lily
Hosta lancifolia
Hosta marginata
Hosta undulata 'Variegata'
Hydrophyllum virginianum; Virginia waterleaf
Iris siberica; Siberian iris
Monarda didyma; bee balm
M. fistulosa; wild bergamot
Myrrhis odorata; Sweet Cicely 'Yellow Cheerfulness,' 'Geranium,' 'Tete a Tete,' 'Sundail,' and 'February Gold' (Ohio)
Oenothera fruticosa; sundrops
Onoclea sensibilis; sensitive fern
Osmunda cinnommea; cinnamon fern
Peaonia species; Peony some (Ohio)
Phlox paniculata; summer phlox
Podophyllum peltatum; Mayapple
Polemonium reptans; Jacob's ladder
Polygonatum commutatum; great Solomon's sea
Primula xpolyantha; polyanthus primrose
Pulmonaria; lungwort
Ranunculus; Buttercup (Abraham)
Sanguinaria canadensis; bloodroot
S. canadensis; 'Multiplex', double-flowered bloodroot
Sedum acre; gold moss
S. spectabile
Stachys byzantina; lamb's ear
Tiger Lily (Abraham)
Tradescantia virginiana; spiderwort
Trillium cernuum; nodding trillium
T. grandiflorum; wide wake-robin
Uvularia grandiflora; big merrybells
Viola canadensis; Canada violet
Viola sororia; woolly blue violet
Bulbs:
Chioniodoxa lucilae; glory-of-the-snow
Crocus
Endymion hispanicul; Spanish bluebell
Eranthis hyemalis; winter aconite
Galanthus nivalis; snowdrop
Hyacinthus; 'City of Harlem'
Muscari botryoides; grape hyacinth
Narcissus; 'Cheerfulness', 'Yellow Cheerfulness', 'Tete a Tete', 'Sundial', and 'February Gold'
Scilla siberica; blue squill
Tulipa Darwin; 'White Volcano', 'Cum Laude', Parrot 'Blue Parrot', and Greigii 'Toronto'
Trees:
Acer negundo; Boxelder (Ashleaf Maple) (Dawes)
Acer nigrum; Black maple (Dawes)
Acer palmatum; Japanese maple
Acer palmatum; 'Dissectum', cutleaf Japanese maple
Acer saccharum; Sugar maple (Dawes)
Asimina trioba; Pawpaw (Dawes)
Betula nigra; 'Heritage", Heritage River Birch (Dawes)
Catalpa bignoiides; common catalpa
Celtis occidentalis; common hackberry (Dawes)
Cercis canadenis; Eastern redbud (Ohio)
Cornus florida; Flowering dogwood (Dawes)
Gleditsia triacanthos f. Inermis; Thorny honey locust (Dawes)
Halesia carolina; Carolina silverbell (Dawes)
Ilex opaca; American holly (Dawes)
Juniperus chinensis; 'Pfitzeriana', Pfitzer Chinese juniper (Dawes)
Juniperus virginiana; Eastern red cedar
Koelreuteria paniculata; Goldenrain tree (Dawes)
Lindera benzoin; Spicebush (Dawes)
Liquidambar styraciflua; Sweetgum (Dawes)
Morus alba; White mulberry (Dawes)
Tsulga canadensis; Canadian hemlock
Peach, Nectarine, Cherry, Plum (Ohio)
Picea abies; Norway Spruce (Abraham)
Pinus jeffreyi; Jeffery pine (Dawes)
Platanus occidentalis; Sucamore (Dawes)
Populus species; Poplar (Dawes)
Prunus serotina; Black Cherry (Abraham)
Prunus species- Cherry (Ohio)
Pyrus calleryana; Callery Pear (Dawes)
Pyrus species- Pear (Ohio)
Quercus alba; White oak (Dawes)
Quercus imbricaria; Shingle Oak (Dawes)
Quercus rubra; Northern red oak (Dawes)
Robina pseudoacacia; Black locust (Abraham)
Sambucus canadensis; American elderberry
Tilia platyphyllos; Bigleaf linden (Dawes)
Viburnum lantana; Wayfaring tree viburnum
Vines and Shrubs:
Clematis; 'Red Cardinal'
Daphne mezereum; February daphne
Euonymus species (Ohio)
Forsythia suspensa; Weeping forsythia
Hawthorn (Abraham)
Hibiscus syriacus; rose of Sharon
Hydrangea, blue (Abrahamr)
Juniper, common (Abraham)
Kerria japonica; Kerria, 'Pleniflora', double-flower kerria (Dawes)
Kolkwitza; Beautybush (Abraham)
Lonicera maackia; Amur honeysuckle (Dawes)
Lonicera tatarica; Tartarian honeysuckle
Lonicera xylosteum; European fly honeysuckle (Dawes)
Morus; White Mulberry (Abraham)
Multiflora rose (Abraham)
Parthenocissus quinquefolia; Virginia creeper
Philadelphus; Mock orange (Abraham)
Rhododendron Exbury hybrids 'Gibraltar' and 'Balzac'
Rhododendron periclymenoides; Pinxterbloom (Ohio)
Rubus occidentalis; Black Raspberry (Ohio)
Syringa; Lilac (Abraham)
Thuja soecies; Arborvitaes (Ohio)