It's a serious outlier
122 isn't quite unbelievable, but it's hard to believe.
Here's a simple chart of oldest living people:
http://www.grg.org/SC/SCChartsGraphs.html
Calment is an utter outlier, and yes, outliers happen, but the mortality cliff at these ages is massive. Like, she's literally off the charts by a fair ways compared to any other supercenetarian. How unlikely? Well, one published stat is that of people who live to 100, only one in 1000 lives to 110. Solve for 122, and Calment becomes...unexpected.
The second reason to doubt the Calment record is that many other supercenetarian records have been wrong, and supercenetarian claims may be clustered around...regions with bad birth records, and regions with relatively poor life expectancy and relatively high crime rates (greetings, Okinawa!).
Is this the crime of the century? No. But if you're studying supercenetarians and trying to figure out what Calment means as a data point, "not real" is the parsimonious explanation.