The Gunners fought back from 2-0 down to force extra-time in Sweden on Saturday thanks to Lioness striker Alessia Russo and Jen Beattie's last-gasp header that cancelled out an earlier quick-fire second-half brace from Mathilde Bourdieu.
A superb second effort from Russo then drew Arsenal level again at 3-3 in an extra-time thriller after Louise Fleury had restored the Paris lead, but Jonas Eidevall's side eventually succumbed 4-2 on penalties after Paris goalkeeper Chiamaka Nnadozie denied both Russo and Frida Maanum.
It is a shock early exit from Europe for Arsenal, who reached the semi-finals of last season’s Champions League before being edged out 5-4 on aggregate by Wolfsburg in heartbreaking fashion.
Eidevall’s team, who open the new WSL campaign at home to Liverpool on October 1, had been full of confidence after brushing aside Swedish side Linkopings in the semi-final of the first round of Champions League qualifying on Wednesday.
Paris FC now advance to the second round of qualifying, where the winners will seal their place in this season’s group stage.