Prestashop
Tag Manager
Tag Manager can be installed in the theme's header template file.
\themes\<<theme>>\header.tpl
Conversion Tracking
This can be done but using the free Plugin that hooks onto the order page:
https://bitbucket.org/ed_eichman/prestashop-gtm-data-layer-module/src/
Download the files and make sure it is in the modules folder. the folder structure should be:
\modules\datalayer\
Then the module will need to be installed. If the module does not show up, you may not have permissions even if you are set up as admin & can see the modules.
Check Module Install Permissions
To check if the account has install permissions use adminer and access the database.