The Lionesses lost Mary Earps to injury in the opening minutes but rallied well and took the lead when Mead put the finishing touch to a fine move which started inside her own half.
But France hit back just before the break through Elisa De Almeida and struck the killer blow 20 minutes from time when Marie-Antoinette Katoto swivelled well inside the box, extending Les Bleues’ lead to five points at the top of the group.
England sit third following Sweden’s victory over Republic of Ireland but can make amends quickly, with a revenge mission set for Saint-Etienne on Tuesday.
The Manchester United star winced after playing a routine pass to Millie Bright and though initially soldiering on, she was replaced after just eight minutes by Hannah Hampton.
After an inauspicious start, England settled around the 20-minute mark and the best chance of the early stages fell to Ella Toone, who met Lauren Hemp’s cutback with a sweeping effort which crept agonisingly wide of the far post.
It was another Hemp cross which led to the opener on the half hour, as former Sunderland player Mead gathered the ball following a scramble in the area before calmly slotting home her 33rd Lionesses goal to move joint-sixth on the all-time scorers list.
Katoto then guided over Delphine Cascarino’s dangerous cross from close range before France produced a deserved equaliser five minutes before half time.
Right back De Almeida turned a poor corner into a great one, meeting the ball on the volley and looping a stunning effort over the helpless Hampton.
England re-asserted themselves before the break and the final chance of the half fell to Mead but her curling effort was tipped behind brilliantly by Pauline Peyraud-Magnin.
France forward Cascarino then side-footed wide early in the second half just moments after the ball refused to sit for Leah Williamson at the other end.
England looked to salvage a point late on but despite some lively moments from substitute Chloe Kelly, France held on for victory in Sarina Wiegman’s 50th game in charge.
Substitutes: 13 Hannah Hampton (Chelsea) for Earps 8’, 14 Fran Kirby (Chelsea) for Stanway 79, 16 Chloe Kelly (Manchester City) for Mead 79
Substitutes not used: 12 Alex Greenwood (Manchester City), 15 Jessica Naz (Tottenham Hotspur), 17 Aggie Beever-Jones (Chelsea), 18 Grace Clinton (Manchester United), 19 Maya Le Tissier (Manchester United), 20 Jess Park (Manchester City), 21 Khiara Keating (Manchester City), 22 Esme Morgan (Manchester City), 23 Millie Turner (Manchester United)
Goals: Mead 30
Bookings: Carter 45+1
France: 16 Pauline Peyraud-Magnin, 5 Elisa De Almeida, 2 Maelle Lakrar, 3 Wendie Renard, Selma 13 Bacha, 14 Sandie Toletti, 7 Sakina Karchaoui, 15 Kenza Dali, 11 Kadidiatou Diani, 9 Marie-Antoinette Katoto, 20 Delphine Cascarino
Substitutes: 6 Amandine Henry for Cascarino 69, 22 Eve Perisset for De Almeida 86, 12 Louna Ribadeira for Katoto 90+1, 10 Lea Le Garrec for Dali 90+1
Substitutes not used: 1 Solene Durand, 21 Constance Picaud, 4 Estelle Cascarino, 19 Thiniba Samoura, 8 Grace Geyoro, 17 Sandy Baltimore, 23 Ines Benyahia, 18 Julie Dufour
Goals: De Almeida 41, Katoto 68
Bookings: Lakrar 70