Even though there is a separate future tense in German, the present tense (Präsens) can also be used to refer to events in the future. So there's nothing in this sentence apart from the word "morgen" that tells us we are dealing with a future event.
That's a difference to English - apart from certain exceptions such as the "timetable future" (The train arrives at four o' clock), the future tense has to be used in English to refer to events in the future.
Speak with - when the person you are in a conversation with someone, when he/she actually talks back.
Speak to - when you speak to a person or group of people who just listen and do not respond in any way, like in a speech or auditorium or symposium.
Without more information, there is nothing wrong with, "I will speak with you tomorrow". "Speak with" and "Speak to" are generally synonymous. However, you will find US English preferring the "speak/talk with" construct and British English more often using "speak/talk to". Consider being at a hotel and asking the bartender how to get to a local attraction, they might say to you, "I'm not sure. You should speak to/with sometime at reception". Both have the exact same meaning. They suggest that there will be dialogue, rather than some unidirectional communication. Having said that, there are specific cases where "speak to" can only mean to address without opportunity for discourse; for example, "The Queen will speak to the nation". You would never use "speak with" in this context.
Since German is pretty complicate, they always look for tricks to make it easier like:
using the present tense instead of the future (it happens in other languages as well... in Italian to some extent... in Japanese always, they even have no future tense as far as I understood)
implying words that can be understood when you use modal verbs
... nothing else pop up to my mind now, but I hope you understood what I mean. :)