Translation:I, too, will learn how to read in French.
Note here, that the use of "тоже" means that somebody else is learning how to read in French, and that the speaker will also be doing the same. If one is learning something already and wants to say that they are also going to learn how to read in French, one would use "также" instead of "тоже".
This distinction does not exist in English.
I agree. In speaking, the distinction is not so much in the word order but in the inflection, so some placements remain ambiguous in writing. "I will also learn to read French"" "I will learn to read French too" These can be pronounced slightly differently to produce either meaning, i.e., stress the "I" or "French") To make it clear in writing I would probably say "I too will learn to read French" if I'm promising to do what someone else is doing. I know this is a bit stiff, but it's unambiguous. "I will learn to read French also" "I will learn to read French as well" "I will learn to read French, too" if I am adding a language to my repertoire. Again, in speaking, this can be made to mean the same as "I too," but in writing, placing the adverb in the predicate is a signal that it refers to the object, not the subject.
You are correct that the same distinction does not exist in English. "I will also learn how to read (in) French" can mean that "I" already read (in) one language and will learn to read (in) French as another one. Yet, the English can also mean that "I" will learn to read (in) French because someone else is learning to read (in) French and I will join them in the endeavour.
When speaking, the distinction may be made by word order and/or intonation. "I, also, will learn how to read (in) French", "I, too, will learn how to read (in) French", or "I, as well, will learn how to read (in) French". "Also", "too", and "as well" are somewhat interchangeable in English depending on word placement (note that "too" can mean "excessive" as in "I ate too much"), and using one or the other wouldn't make the same distinction as the Russian также and тоже. "I will learn how to read (in) French also", "I will learn how to read (in) French too", or "I will learn how to read (in) French as well" - neither one makes any distinction.
Absolutely. Someone should have noted that first thing. I can't imaging anyone using 'in' here unless they are translating. On the other hand, "I am learning to read Racine in French" would be perfectly natural. In the Duo sentence, English would make French the object of the verb, and Russian makes it an adverbial phrase. Different idioms.
Typically when you learn HOW to do something, for example, to read French or to ride a bicycle, use the verb научиться. When you learn or study something academic, for example, a French poem or the design of a bicycle, use the verb выучить.
Я тоже выучу французский стих.
Он научится ехать на велосипеде. Он выучит дизайн велосипеда.