The ranger and druid class feat "Wild Empathy" specifically allows you to improve the attitude of animals.
The spell "Speak with animals" allows you to communicate with animals and ask questions. Does it also allow improving the attitude of animals just like "Wild Empathy"?
Speak with animals basically allows you to skip wild empathy, and use regular social skills, like Diplomacy, to improve the attitude of wild animals. If you have speak with animals, you don’t need wild empathy, and if you have wild empathy, you don’t need speak with animals to improve animals’ attitude.
Nothing about speak with animals will stop you from using wild empathy, however. You can still do that; your DM may even give you a circumstance bonus for doing so (that’s up to them, though; nothing in the spell or feature indicates that they’re “supposed to”).
According to the spell description, at least on Google for 3.5,
You can comprehend and communicate with animals. You are able to ask questions of and receive answers from animals, although the spell doesn’t make them any more friendly or cooperative than normal.
The way I interpret this, the spell won't automatically make them friendly or cooperative, or automatically allow you to improve their mood. However, I don't see why that would stop you from conversing with them using the spell, to improve their mood with your words, which they can now understand due to the spell. Perhaps you could ask your DM if you can make a charisma check to see if you can talk them up to improve their mood.
Not Wild Empathy, but...
Most info is coming from the D20 SRD.
Wild empathy is a ranger class trait that uses ranger levels:
Wild Empathy (Ex) A ranger can improve the attitude of an animal. This ability functions just like a Diplomacy check to improve the attitude of a person. The ranger rolls 1d20 and adds his ranger level and his Charisma modifier
I suspect, though, that you are instead asking about using skill checks such as Diplomacy to improve the mood of animals. This is a rather gray area in the rules. The "Speak With Animals" spell says:
If an animal is friendly toward you, it may do some favor or service for you.(Emphasis mine)
This implies that skill checks on an animal you can speak with are possible, but not what the skills might be. There is a good amount of debate on other forums about Diplomacy vs Handle Animal. On one hand, the handle animal skill only talks about making an animal perform tasks and raising an animal to be loyal. On the other hand the diplomacy skill makes no mention of animals or other non-verbal creatures, and the low intelligence score of animal-type creatures...
Traits
An animal possesses the following traits (unless otherwise noted in a creature’s entry).Intelligence score of 1 or 2 (no creature with an Intelligence score of 3 or higher can be an animal)
May prevent them from understanding the finer points of conversation. So this is very much a DM discretion thing. Diplomacy does reference the wild empathy class trait and uses the same table, so odds are somewhat favorable for that being your answer.
