Thank you for those first answers. As I have poor knowledge of coding, it'll take time before I meet a result.
My research led me to a plugin (Layout loader) , which is able when opening the composer to zoom directly to the canevas location. However for certain reasons, I am not likely to use that plugin, and so I'll carry on with your solutions.
Here is the link to the plugin : link to Github
And here, an extract of the code:
# Get current canvas extent and apply that to all maps (items) in layout
# Replace any text "{{title}}" in any layout label with the dialog Title text
canvas = iface.mapCanvas()
for item in l.items():
if item.type()==65639: # Map
item.zoomToExtent(canvas.extent())
if item.type()==65641: # Label
item.setText(item.text().replace('{{title}}',title_text))