It is clear that Xabi Alonso being new to Real Madrid needs time to fully connect with team and put his plans into action. For him to achieve high goals at Real Madrid it is vital he builds strong relationships and truly understands his players.
It is understandable he has not yet picked all his ideal players or perfected his strategies as this takes patience. However once he is fully integrated and team works well together under him they have great chance of success. Giving him more time looks like smart decision given their current performance and future looks bright for Real Madrid with him in charge.
I don't think Real is the team that is ready to give the coach a lot of time to adapt. Look at Ancelotti's example, it is obvious that the team faced big problems in defense last season, and still I think that they did not have a catastrophically bad season, although they were left without trophies, but despite this no one gave him time to fix the situation, he was fired. For Alonso, I think even less time will be given, and this defeat to PSG already shows that he was unable to achieve a quick effect, old problems remain and if the start of the season is unconvincing, then he will not stay long at Real.