There is not only one twig template, there are three levels of twig templates in a field collection field:
1) The field template for the field-collection field:
2) The field-collection template itself:
3) The field templates for the fields inside of the field collection:
When you are in the top level, the fields of the field collection are not built yet and you have no access to the rendered fields.
The best approach is probably to put the table structure in all three levels, in 1) the header and footer, in 2) the row and in 3) the cells.
There is one problem with this approach. In 1) you don't have the labels for the header. If you don't want to hardcode them, you can try to get them from the configuration of the field collection in a preprocess hook.