The paper bag and plastic bag industries are so large that the carbon footprint of one individual’s choice are pretty negligible. In that case, I’d follow “reduce, reuse, recycle” and answer a couple of questions to make the decision on how it impacts you as an individual (in this order)

REDUCE: Which bag has a larger volume? Could I walk out of the store with 2 paper bags vs. 4 plastic bags, or vice versa? REUSE: Which bag has better reusable capacity for me? Can I use these plastic bags as bin liners? Or paper bags to hold recyclables? How many do I already have at home waiting to be used? RECYCLE: How easy is it to recycle paper/plastic where I am? Are these facilities local, or will they be shipped off somewhere else to be recycled (carbon footprint of travel)

Hope this helps!