Which theme you are using?
Because accordingly, I can suggest you in the liquid where you can put this message.
On which page you want to show a Free shipping message?
Means on the home page, collection page?
Let me know.
This is an accepted solution.
For collection pages. Please add following code in your sections/product-card-grid.liquid file
For the product page. Insert the same code in sections/product-template.liquid file.
Let me know if this works.