Wireless phone is busy, not working.

OK...
So let’s forget it, there is no way to make both A116 work together except to connect them both to the box.


However, it is possible if you have a Livebox Play ======>
to directly connect one or two Philips handsets to the Livebox.
Procedure to try

1 On the Philips handset select [Menu] >[Services] > [Subscribe], then press [OK] to confirm.

2 on the Livebox Play press the button located at the back ====>

3 On the Philips handset, enter the system PIN code (0000). 
Press [Delete] to correct. 
Then press [OK] to confirm the PIN code.

Once the above procedure is completed, the Philips handset will theoretically work like the Gigaset...
However, some features of the Philips may be missing

The D450/455 manual: https://download.p4c.philips.com/files/d/d4550b_12/d4550b_12_dfu_fra.pdf

and following your advice, that is by connecting the second one next to the first, to the electrical socket only, since the other is already connected to the Orange box, I get nothing but a "busy" signal...
Thank you anyway for trying to help me!

Furthermore, you say two Gigaset A116 solo... isn't it an A116 duo?

Is the phone near the box properly connected to the box with a cable to the phone socket of the box?
What does the handset that doesn't work display?
Something like this:
Describe any differences or additional displays.

Then swap the handsets, placing the non-working handset in the place of the working one.
What happens?

Well, I think I finally understood
The two bases of your A116 are connectable to the box.
You have two A116 bases and not one A116 base with an additional handset (in other words, an A116 duo).

Please confirm that these are indeed two A116 bases.

The problem is that both bases need to be connected to the box... because this model does not allow for an additional handset...
The manual is silent on this matter. Confirm that there is no button on the base, and check that the menu on a handset matches what is described on page 21 of the manual.

Edit: Check that you do not have Menu --> Settings --> OK --> Handset --> OK --> Register handset

The manual: https://gse.gigaset.com/fileadmin/legacy-assets/CustomerCare/Manuals/A1xx_A2xx_A3xx_AL1xx_AL2xx_AL3xx/A116/A31008-M2801-R101-1a-8N19_fr_BE-FR.pdf

Then, what do you have left from the Philips D450? A working handset?
If so... we can probably connect it directly to your Livebox Play wirelessly.

Solos cannot work; you need duos.
The Gigaset A116 is a solo that does not allow the pairing of another handset with its base.

On the other hand, the Phillips does have a way to connect to a DECT base... The Livebox Play allows this association. Once the procedure is completed, it serves as a base for the handset... without being connected to the box via a cable.
That's why... I suggest connecting the A116 to the Livebox and "pairing" the Philips with the Livebox... You will have 2 phones that will work.
One wired, the other wireless, which can therefore be installed anywhere on its charger..

Glad you finally resolved the issue.
Your thanks are my only "reward."
The contributors on the CCM forums are volunteers.
Have a great rest of the day.