7" wide usually means between the bead seats.  Offset is measured at the center plane of the wheel and usually in MM.  If you lay the rim down and measure from the ground to the top edge (total width), you can generally add almost an inch.  Back space is measured using the total width, using inches.  Most Avanti II rims I've seen(15X6 or 7" total width) have a +15mm offset, which means the backspace on those would be about 4.125". (7/2 = 3.5" and 0MM offset   4.125 - 3.5 = .625 or 5/8" or 15mm.  SO,  if you have 7 inch rims, they're close to 8" wide and at 0 offset you would have 4.0" backspace.  These will fit on your car, but be close to the fenders. If you hit a bump in a turn they could hit.
It's always advisable to use the same offset, as the original rims, when going to larger width rims, in order to keep the weight even on the wheel bearings.  I followed this to a tee and the 16X7 rims on my car are fine, except in a full crank, left turn, the right upper, outer grease fitting gets rubbed  by the rim.  I remedied this by removing the fitting and installed a plug.
If I opted to use a zero offset rim, the tire would have been much closer (5/8") to the fender.
 There's also the possibility of the tie rod end hitting the tire, if you use a low profile (60 or 65 series) with a 7-8" rim