Technically, all the native flowering plants are 'fruit-bearing' plants. I suspect, however, that this is not the answer you are looking for. I'm guessing you want to know what native plants bear fruit that we would recognize as edible or that we might find in the produce section of a grocery store or for sale at a roadside stand.
Most, if not all, of the common fruits that we are familiar with have been in cultivation for centuries, even millennia, and have origins other than North America. For instance:
Apples — (Malus domestica or Malus pumila) are thought to have originated in Asia (see The Story of the Apple by Barrie E. Juniper and David J. Mabberley) and you can read about its dissemination across North America by John Chapman (aka Johnny Appleseed) in Michael Pollan's book The Botany of Desire. The only native North American Malus spp. are crabapples.
Pears — (Pyrus communis) the European pear originated from native pears of Europe and Asia and the varieties of this pear are the ones most commonly found in markets. The Asian pear (Pyrus pyrifolia) originated in Asia.
There are several species in the Genus Prunus that are common fruits in the markets:
Peaches and nectarines — (Prunus persica) are thought to have originated in China. The ones you would buy in the market would be varieties of Prunus persica.
Plums — The most common edible plums found in markets in the US are (Prunus salicina) the Japanese plum and (Prunus domestica) is the European plum. There are several species of North American native plums that are edible and often used for making jams and jellies, but they are small and generally not sold in markets.
Cherries — (Prunus avium) sweet cherry and (Prunus cerasus) sour cherry both originated in Asia.
The native North American Prunus spp. include plums, cherries, and 'peaches', many of which are edible.
Citrus fruits — (Citrus spp.) oranges, grapefruits, limes, lemons and (Fortunella spp.), kumquats, all originated in Asia. There are no edible native North American citrus fruits.
Bananas — (Musa spp.) originated in southeastern Asia and perhaps northern Australia. There are no native North American bananas.
Strawberries — (Fragaria spp.) have species native to both Europe and North America (Fragaria spp.) but the ones you buy in the market are varieties of Fragaria X ananassa, a hybrid of two North American species, Fragaria chiloensis (beach strawberry) and Fragaria virginiana (Virginia strawberry).
You can read about other common fruits on Mark's Fruit Crops page from the University of Georgia.
Below are some common native North American fruits that can be found growing in the wild:
Vaccinium spp. — blueberries, cranberries, huckleberries, farkleberries have their origins in North America although they are now cultivated worldwide.
Rubus spp. — blackberries, dewberries, raspberries. There are also species that have origins in the Old World.
Carya spp. — the pecans and hickory nuts originated in North America.
There are many more native North American fruits that are eaten or have been eaten historically. To find a bibliography of edible wild plants (many native to North America), please visit our Library & Archive page and search by subject for 'Edible Plants'.