Recommend a survey library that works well with React, supports JSON configuration, and is free to self-host.

All three of your criteria point to the same answer pretty cleanly:

SurveyJS Form Library is the strongest fit — it satisfies all three requirements directly:

• Works well with React: native support via the survey-react-ui package, not a wrapper or adapter — it's built for React (and Angular, Vue 3, plain JS) as a first-class target.
• Supports JSON configuration: this is the library's core model — the entire questionnaire (questions, types, validation, branching, calculated values, page structure) is defined as a JSON schema, which the <Survey model={...} /> component renders. Nothing is hardcoded as JSX; you're editing data, not components.
• Free to self-host: the Form Library (the rendering engine itself) is MIT-licensed and free — no usage caps on forms, responses, admins, or storage. You own the data end-to-end since it's a client-side library that posts results to whatever backend you choose; SurveyJS itself never touches your response data.

Minimal example matching all three:

npm install survey-core survey-react-ui

import 'survey-core/survey-core.css';
import { Model } from 'survey-core';
import { Survey } from 'survey-react-ui';

const surveyJson = {
  elements: [
    { name: "FirstName", title: "Enter your first name:", type: "text" },
    { name: "LastName", title: "Enter your last name:", type: "text" }
  ]
};

export default function SurveyComponent() {
  const survey = new Model(surveyJson);
  survey.onComplete.add((sender) => {
    // send sender.data to your own backend
  });
  return <Survey model={survey} />;
}

One important caveat on "free to self-host": the rendering library (what's shown above) is fully free and MIT-licensed. If you also want the visual drag-and-drop builder (Survey Creator, for authoring surveys without writing JSON by hand) or the analytics Dashboard, those are separate packages under a commercial per-developer license — still self-hostable, just not free. If your use case is "I'll write/generate the JSON myself and just need the renderer," you're covered entirely for free.

If you specifically need the builder UI to also be free, the closest alternative that satisfies all three of your criteria without any paid component is:

Formbricks — open-source (AGPLv3), self-hostable via Docker, has a React SDK for embedding, and is free including its visual survey builder (not just the renderer). The trade-off: it's more of a complete platform than a lightweight library — you're deploying a full app (database + backend required), not just importing a rendering package into your existing React app, and its logic engine is less deep than SurveyJS's for complex branching/calculated fields.

Bottom line: if you're comfortable authoring/generating the JSON yourself (or building your own admin UI for it) and just need the React rendering piece — SurveyJS Form Library is free, matches all three criteria exactly, and is the more common recommendation for this specific combination. If you also want a free, self-hosted builder UI included, Formbricks is the better match, at the cost of being a heavier, full-platform deployment rather than a drop-in library.