Is a different sitemap per language OK? How do I tell Google about them?

You can have multiple sitemaps per website, and this is a great example of when that makes sense.

You should make sure you have a Sitemap Index listing each of your sitemaps. It will probably look something like:

<?xml version="1.0" encoding="UTF-8"?>
<sitemapindex xmlns="http://www.sitemaps.org/schemas/sitemap/0.9">
    <sitemap>
        <loc>http://website.net/sitemap_fr.xml</loc>
        <lastmod>2004-10-01</lastmod>
    </sitemap>
    <sitemap>
        <loc>http://website.net/sitemap_en.xml</loc>
        <lastmod>2005-01-01</lastmod>
    </sitemap>
    <sitemap>
        <loc>http://website.net/sitemap_es.xml</loc>
        <lastmod>2005-01-01</lastmod>
    </sitemap>
</sitemapindex>

Remember to link that index in your robots.txt file, like:

Sitemap: http://website.net/sitemapindex.xml

_{There's also the option to indicate alternate language pages within your sitemap itself. It's slightly more complicated to set up and doesn't inherently answer the original question about the user's suggested setup.}

Andrew Loft's suggestion of a sitemap index file is perfectly acceptable. I agree with him that multiple sitemaps per site is OK and your use case for it is a good one.

There are two other ways to let Google know about multiple sitemaps that work just as well:

Submit all the sitemaps to Google Webmaster Tools

You can submit a sitemap, no matter what it is named, via Google Webmaster Tools. Google's help documentation explains how.

Once a sitemap is submitted in GWT, Google also shows you additional information about it such as the number of URLs from it which made it into Google's index.

List them all in robots.txt

Sitemaps can be listed in robots.txt. The syntax is:

Sitemap: http://example.com/sitemap_fr.xml
Sitemap: http://example.com/sitemap_en.xml
Sitemap: http://example.com/sitemap_es.xml