My first thought was Fox grape as @plantladylin
This plant grows where I live and the leaf shape is variable.
There is also a Mustang grape.
If you could take photos showing the back side of the leaves that might help. Also feel the back to see if they are 'furry' (sorry I don't know the botanical name for that).
Either way, these grapes grow because birds and other animals eat the grapes and deposit the seeds. There were some wild grapes near me that my neighbor found quite edible. When the county maintenance men were trimming back all the vegetation from along the fenceline at the school they never cut back the grapes as they recognized them as edible. I think if yours get enough sunlight the taste may be okay.
When someone plants grapes they usually plant in a very sunny location. Most of the time there will be some kind of support such as an arbor, trellis, etc.