At no point does it say they weren't having an affair though.
These "newspapers" wouldn't be publishing an apology if they had any proof whatsoever that they were having an affair. As soon as her lawyers came to them and said "We will sue" did they offer this half-hearted apology.
And actually they are now saying it was all bollocks;
On January 31, we published some personal information about Vanessa Perroncel concerning an alleged affair
This affair was alleged by the tabloids themselves
with the footballer John Terry. We have since been informed she would have preferred this to remain private and it was untrue in any case
You can be pretty sure that the tabloids lawyesr went over this statement before they posted it and the way it reads is that there was nothing happening here and they indeed just decided to make the story up themselves.