It could be relatively easily tested by measuring the ratio of C14O2 to C12O2 in the atmosphere, vs. the same ratio in, say, wood of an exactly known age from, say, the 18th century. By reversing the known decay rate of C14, the ratio in the pre-industrial 18th century could be calculated.
Since all the fossil fuel that has been burned since the 19th century has had 0.000% C14, the current ratio of C14O2 to C12O2, all things being equal, should be "much" lower, if your hypothesis is correct.
My best guess is that some of each ratio change (13/12 and 14/12) is natural and some is from fossil fuel burning. In the case of 14/12, one natural factor is high solar activity in the late 20th century. But most of the rise is fossil fuels. For 13/12, some of the ratio change is natural because some natural sources mimic the fossil fuel ratio (e.g. deep ocean). Dr Spencer also has some thoughts on 13/12 http://wattsupwiththat.com/2008/01/28/spencer-pt2-more-co2-peculiarities-the-c13c12-isotope-ratio/ answered by Englebeen who says that vegetation and fossil fuels show a similar ratio (due to growing plants preference for C12).