Background: In the context of the SARS-CoV-2 pandemic, our interest was to evaluate the effect of COVID-19 during pregnancy on placenta and coagulation factors. Methods: a prospective cohort study between January and July 2021 of 55 pregnant women stratified into: Group O, 16 patients with ongoing SARS-CoV-2 infection at delivery; Group R, 21 patients with a history of SARS-CoV-2 infection during pregnancy but who recovered prior to delivery; Group C, 18 control patients with no infection at any time. All women had nasopharyngeal SARS-CoV-2 RT-PCR tests performed within 72 h of delivery. Obstetrical complications were recorded and two physiological inhibitors of coagulation, protein Z (PZ) and dependent protease inhibitor (ZPI), were analyzed in maternal and cord blood. All placentae were analyzed by a pathologist for vascular malperfusion. Results: No patient in any group had a severe COVID-19 infection. More obstetrical complications were observed in Group O (O: n = 6/16 (37%), R: n = 2/21 (10%), C: n = 1/18 (6%), p = 0.03). The incidence of placental vascular malperfusion was similar among the groups (O: n = 9/16 (56%), R: n = 8/21 (42%), C: n = 8/18 (44%), p = 0.68). No PZ or ZPI deficiency was associated with COVID-19. However, an increased ZPI/PZ ratio was observed in neonates of Group R (O: 82.6 (min 41.3–max 743.6), R: 120.7 (29.8–203.5), C: 66.8 (28.2–2043.5), p = 0.04). Conclusion: COVID-19 was associated with more obstetrical complications, but not an increased incidence of placental lesions or PZ and ZPI abnormalities.