Inclusion Criteria:  Age > 18 years  Patient with septic shock for less than 24 hours, defined according to The Third International Consensus Definitions for Sepsis and Septic Shock (Sepsis-3) by the combination of:  Sepsis defined as organ dysfunction caused by an inappropriate host response to infection (increase in SOFA score of at least 2 points secondary to infection), Persistent hypotension requiring vasopressor drugs to maintain mean arterial pressure ≥ 65 mmHg, Serum lactate level > 2 mmol/l despite adequate vascular filling. Hemodynamic stability for >30 min with mean arterial pressure ≥ 65 mmHg and noradrenaline dose ≤ 0.5 μg/kg/min, Consent signed by the patient, family member, or legal representative or inclusion under emergency procedure, Negative to a diagnostic test for SARS-CoV2 less than 72 hours old; the test used must be on the the list published on the Ministry of Solidarity and Health website  Non-inclusion Criteria:  Current treatment with steroids or other treatment that may affect the hypothalamic-pituitary-adrenal axis, Anesthetic induction with etomidate within 6 hours prior to randomization given its selective inhibitory effect on 11 β-hydroxylase, Known hypersensitivity to fludrocortisone (or any of its excipients), or to tetracosactide (Synacthen®), Disturbed gastric emptying (gastric residue > 500 ml) in the absence of an alternative route of administration available (naso-jejunal tube or jejunostomy), Pregnant or nursing woman, Patient participating in another trial, possibly interfering with the study procedures, Person not affiliated to a social security system, Known situation of deprivation of freedom (safeguard of justice), guardianship or curatorship, Patient with a life expectancy of less than 24 hours. Patient with known or suspected SARS-CoV2 pneumonia  Exclusion criteria:  Patients under court protection will be excluded as soon as the investigator is aware of their status. Hemodynamic worsening with noradrenaline dose >1.5 μg/kg/min before evaluation of the primary end point. Catecholamine withdrawal before evaluation of the primary end point.