You can use the _getexif()
protected method of a PIL Image.
import PIL.Image
img = PIL.Image.open('img.jpg')
exif_data = img._getexif()
This should give you a dictionary indexed by EXIF numeric tags. If you want the dictionary indexed by the actual EXIF tag name strings, try something like:
import PIL.ExifTags
exif = {
PIL.ExifTags.TAGS[k]: v
for k, v in img._getexif().items()
if k in PIL.ExifTags.TAGS
}