How can I make sure that my JavaScript files delivered over a CDN are not altered?

As a matter of fact, a feature like this is currently being drafted under the name of Subresource Integrity. Look into the integrity attribute of the <script> tag. While not yet fully adopted across the board, it fulfills just this purpose.

integrity

Contains inline metadata that a user agent can use to verify that a fetched resource has been delivered free of unexpected manipulation. See Subresource Integrity.

Source

Subresource Integrity (SRI) is a security feature that enables browsers to verify that files they fetch (for example, from a CDN) are delivered without unexpected manipulation. It works by allowing you to provide a cryptographic hash that a fetched file must match.

Source

Example:

<script src="https://example.com/example-framework.js"
    integrity="sha384-oqVuAfXRKap7fdgcCY5uykM6+R9GqQ8K/uxy9rx7HNQlGYl1kPzQho1wx4JwY8wC"
    crossorigin="anonymous"></script>

Note however that this will not protect you against Man in the Middle attacks if you are transferring your resources via plain HTTP. In this case, the hash code can be spoofed by the attacker, rendering the defense against manipulated script files useless.

For this reason, you should always use secure HTTPS connections instead of plain HTTP in addition to the security measures described above.