If I send an invoice to my client on SY, do I have to keep a paper copy of the invoice?

No. There is no longer a paper original. This is the invoice in its electronic format that constitutes the original and is to be kept for the legal archiving or preservation period. 

CEGEDIM archives electronic invoices CEGEDIM on your behalf if the electronic invoices are signed electronically.

CEGEDIM do not archive invoices not signed electronically (i.e. in simple PDF mode). In this case, you are responsible for archiving them during the legal period.