Which tense is this?

The phrase got omitted due to some reason. I'll re-paste it here: 

"Cette semaine, le museé a anoncé que l'art allait être restauré à partir de février prochain." 

This is an interesting question, and I hope we get an answer from one of the native speaker experts.

It's a question of reported speech, where the tense is normally changed ("backshifted") from the original speech when it gets reported. So typically the museum spokesman says "The art will be restored" and this gets reported as "He said that the art was going to be restored". 

This backshift is characteristic of reported speech in both French and English. But, at least in English, it doesn't always happen. The backshift is optional if you know that the statement is still true (i.e. still in the future in this case) when you report it. 

In this case we're told it's from next February, so it must still be in the future. Therefore in English we'd probably say "This week, the museum announced that the art will be restored from next February." 

If, instead, you said "This week, the museum announced that the art was going to be restored from next February." it might imply that it's no longer true - e.g. the museum has had to cancel it's plan for lack of funding.

I'd be interested to know whether this is also true in French.

Mille mercis, Alan! :) What you're saying is making sense to me. I'm going with this explanation until a native expert contests it. 

In English, we have essentially the same basic rules about changes in tense, but there a lot of exceptions. To achieve native speaker fluency in English, you have to go beyond those basic rules. 

In general, reported speech seems to be similar in French and English, but I imagine there must be some differences. Perhaps we are more flexible in deciding whether to backshift in English? I hope the coming lesson will discuss these differences.

Merci, Cécile! It's a lot more clearer now. Looking forward to the lesson on Reported Speech.