Algolia doesn't offer a supported prebuilt extension or plug-in for PrestaShop.
PrestaShop is built with PHP, and Algoia does provide a PHP client[1], which could be used to build a custom extension to integrate with Algolia on the server-side, Algolia also offer JavaScript[2], React[3] and Vue[4] for client-side development.
Links
[1]: https://www.algolia.com/developers/search-api-php
[2]: https://www.algolia.com/developers/web-instantsearch-vanilla-js
[3]: https://www.algolia.com/developers/mobile-web-instantsearch-react
[4]: https://www.algolia.com/developers/web-instantsearch-vue