I assume with "org" and "fr" you mean the root folders of your site web script paths, like in "org/alfresco/components/form/controls/". Where to put which file depends on which one of these you want to override or provide an alternative for.
If you want to override picker.inc.ftl without having to adapt/override all of the templates that include it, you have no choice but to put the template in ./webapps/share/WEB-INF/classes/aflresco/site-webscripts/org/alfresco/components/form/controls/common/ - you cannot put it in a "fr"-rooted path, unless you also override all other templates and change the relative include directive to an absolute path.
If you want to provide an alternative for picker.inc.ftl, you can put it anywhere and just have to make sure that the path you use in the include directive of whatever template needs it properly resolves to the template.
If you want to override the category.ftl, you can put it into the configuration path using the ./alfresco/web-extension/site-webscripts/org/alfresco/components/form/controls/ path - that way all existing uses of category.ftl would be transparently adapted.
If you want to provide an alternative to category.ftl, you can put it anywhere and just have to make sure that you use the correct path inside your Share config XMLs as the control template for your form fields.