Inclusion Criteria:
* Are diagnosed with chronic heart failure with New York Heart Association Class II-III (Heart Failure) HF symptomatology at screening and on guideline-directed HF therapy for at least 6 months prior to screening.
* Have not changed optimal guideline-directed HF therapy, either medication or medication dose, in the last 4 weeks prior to screening and during screening period, and do not plan to change HF therapy for the next 90 days.
* Must be on a stable dose of vasodilator therapy for at least 4 weeks prior to screening, with no dose adjustments planned during the study.
* Have an estimated glomerular filtration rate of greater than or equal to (≥) 30 milliliter per minute per 1.73 square meters (mL/Minute/1.73m²) at screening.
* Are between 30 days and within 12 months from recent heart failure hospitalization to screening.
* Have systolic blood pressure (SBP) greater than (\>) 110 millimeters of mercury (mmHg) at screening and at enrollment.
* Have a body mass index within the range of 18.5 to 40 kilograms per square meter (kg/m²) (inclusive).
* Are individuals assigned male or female at birth, who are not of childbearing potential.
* Have venous access sufficient to allow blood sampling.
* Applicable to heart failure with preserved ejection fraction (HFpEF) participants only
* Have left ventricular ejection fraction (LVEF) \>45 percent (%).
* Left atrial volume index \>34 milliliters per square meter (mL/m²) in participants in sinus rhythm, or \>40 mL/m² in participants with atrial fibrillation (AF).
* N-terminal pro-B-type natriuretic peptide (NT-proBNP) \>300 picograms per milliliter (pg/mL) for participants without AF or \>850 pg/mL for participants with AF.
* Have a documented history of signs, symptoms, or both, consistent with HFpEF.
* Applicable to heart failure with reduced ejection fraction (HFrEF) participants only:
* Have LVEF \<40% .
* NT-proBNP \>600 pg/mL for participants without AF or \>900 pg/mL for participants with AF.
* Have a documented history of signs, symptoms, or both, consistent with HFrEF.
Exclusion Criteria:
* Have known allergies to related compounds of LY3971297 or any components of the formulation, or a history of significant atopy.
* Had a myocardial infarction, unstable angina pectoris, coronary artery bypass graft surgery, revascularization or other major cardiovascular surgery, stroke, or transient ischemic attack in the last 90 days prior to screening.
* Have New York Heart Association (NYHA) Class 4, acute decompensated HF (exacerbation of HF) requiring IV diuretics, IV inotropes, or IV vasodilators, within 30 days prior to screening, and/or during screening period until randomization.
* Have SBP ≥180 mmHg at screening.
* Have symptomatic hypotension.
* Have resting heart rate \>90 beats per minute (bpm) at screening.
* Have known cardiac amyloidosis, infiltrative myocardial diseases, muscular dystrophies, cardiomyopathy with reversible causes, hypertrophic cardiomyopathy, pericardial constriction, or complex congenital heart disease.
* Have any history of moderate-to-severe stenosis of the mitral and/or aortic valve or severe mitral and/or aortic regurgitation.
* Have any history of moderate-to-severe tricuspid or pulmonic valve stenosis or severe tricuspid or pulmonic regurgitation.
* Have a history of syncope that, in the opinion of the investigator, may affect the participant's safety.
* Bioprosthetic valve replacement within 12 months prior to screening or any history of mechanical valve replacement, or planned valve replacement or repair during the study period.
* Have any history of greater than moderate pulmonary hypertension.
* Have a pacemaker or implantable cardioverter-defibrillator placement within 90 days prior to screening.
* Have severe chronic obstructive pulmonary disease (COPD).
* Have clinically significant or uncontrolled cardiac arrhythmia.
* Have a significant history of, or presence of, hepatic disease, including any abnormal liver function tests.
* Have, within 3 years prior to screening, a history of an active or untreated malignancy or are in remission from a clinically significant malignancy (Exceptions: basal or squamous cell skin cancer).
* For US sites: have donated blood of more than 500 mL within the previous 90 days of screening or intend to donate blood during the course of the study.
* For Japan sites: have donated any blood within the last 4 weeks, any apheresis (blood components) within the last 2 weeks, at least 400 mL of blood within the last 16 weeks for female participants or 12 weeks for male participants, or at least 800 mL of blood for female participants or 1200 mL of blood for male participants within 12 months.
* Other sites: Participants who have recently donated blood or blood components, or who intend to donate during the course of the study.
* Have not been on a stable dose of medications for at least 4 weeks prior to screening, or have planned dose adjustments during the study.
* Participants must abstain from taking new prescription or nonprescription drugs.
* Have concurrent use or intend to use phosphodiesterase 5 inhibitor or soluble guanylyl cyclase activators.
* Have any history of intolerance to vasodilator medications that, in the opinion of the investigator, would put them at risk of not tolerating study drug.
* Have BP and/or pulse rate constituting a risk when taking the Investigational Medicinal Product (IMP).
* Are diagnosed with orthostatic hypotension.
* Show evidence of an acute infection with fever or infectious disease at screening.
* Applicable to HFrEF participants only
* Have been listed for cardiac transplantation and/or anticipated or implanted ventricular assist device.
* Have received cardiac resynchronization therapy for less than 6 months.
