While @Alone-zee is probably correct in that the specific cultural reference, it’s a construct that could literally translated to:

I have tennis

Which can be understood as either one going to play tennis or going to a tennis class but in any case, it’s clear that the subject is going to play tennis.

Here, the second dimension to this is that there is a form of rejection using the pretext of ‘having tennis’.

Finally, in this specific context, it seems that the device is experiencing issues and the software is displaying this message as a multi-layered joke.

1. It’s acting as if the device is rejecting you;
2. Obviously, the device does not ‘have tennis’

As Alone-zee already commented, j’ai tennis is based on a well known humorous lame excuse to tell you won’t be able to attend something.

The phrase means you have a planned tennis match or training.

The original sentence was Nan, j’peux pas, j’ai piscine (Nah, I can’t, I have a swimming lesson), a running joke by Laurent Baffie muppet in Les Guignols de l’info in the nineties (Nulle part ailleurs – Canal+).

Nowadays, piscine can be replaced by any activity, whether sports related or not.

In that particular case, the fast-food restaurant human interface designer joke was possibly inspired by a Fédération Française de Tennis advertising campaign.