Sorting a JavaScript array with a Regex
Contentwise considerations


Use const wherever possible, otherwise let. Avoid var.
Match the version number only once (see code below) and employ the ? operator to save redundancy: v_?[0-9].
(The latter might actually be disputable, I personally find both versions easy to read.)


Your code would be shorter and much easier to reason about if it was more functional.
However, as JS is missing some functional concepts other languages take for granted (array comprehension, min/max in array by key function), this would require helper functions being a new, but onetime overhead. Are you using a third-party library like Lodash by accident? Then you already got many functional polyfills.

Which methods does the Enumerator you are using from SharePoint support apart from the iterative query interface with moveNext(), get_current()? If there is no built-in support, I'd suggest writing a generator function:

function *getTemplateIterator(templates) {
  const templateEnum = templates.getEnumerator();
  while (templateEnum.moveNext()) {
    yield templateEnum.get_current();
  }
}

function ApplyTemplate() {
  return [...getTemplateIterator(this.templates)]
    .filter(template =&gt; template.get_title().includes('espace_projet'))
    .map(template =&gt; {
      const version = /v_?([0-9]+)/.match(template.get_title());
      return {
        version: (version !== null) ? parseInt(version[1], 10) : -1
        template: template
      };
    })
    .reduce((highestVersionedTemplate, template) =&gt;
      (template.version &gt; highestVersionedTemplate) ? template : highestVersionedTemplate,
      { version: -1, template: null }
    );
    // In contrast with an array max/min function suporting a key extracting function
    // (e.g. like in Python: https://docs.python.org/3.8/library/functions.html#max)
    previousChainOfFunctions.maxOrDefault(template =&gt; template.version, { version: -1, template: null });
}


Stylistic considerations


Your variable names are self-explanatory and consistently written, that's fine!
Use consistent braces in blocks (function, if, many more), e.g. function { or function[newline]{, but do not mix both.
Always use braces around if, else, for, while.