I know that Spanish and French both belong to the Romance branch and they are very alike. But what I want to make clear is that how similar they are. I mean that if I have mastered one of them, how much easier will it be for me to learn another one?
French and Spanish are indeed members of the Romance branch, but French is an oddity within it. If you speak only English, the phonetics of Spanish are probably much easier than French sounds, so you'd probably make a quicker start in Spanish. On the other hand, if you learn French first, Spanish would then be relatively easy.
The question "how similar are these two languages" can't be easily answer. There are many levels at which you could make a comparison, and it's not obvious how you want to quantify that. If we're talking just about lexical similarity then the answer is very similar, you can take a look here.
I mean that if I have mastered one of them, how much easier will it be for me to learn another one?
First, knowing two languages instead of only one already makes it easy to learn a third one. At the very least, you won't take the quirks and irregularities of your first language for granted, and will be prepared to expect something different.
Second, learning a language of a given linguistic family definitely makes it easier to learn a further language of that family. This effect is incremental: if you know two languages of a given family, it is even more easier to learn a third one. You will be acquainted to at least part of the lexical entries one needs to learn.
Third, specifically, no, French and Castillian are not particularly similar. If you master Castillian, you will probably be able to read a text in Portuguese or Catalan and understand most of it; but this is not true of French. However, English has borrowed so much lexical entries from French, that a person whose first language is English, and learns Spanish, will probably be in a better position to extract a basic comprehension from a French text than a person whose first language is another one, even another Romance language.
So, in short, learning one of them won't preclude the need of specialised classes to learn the other. Those classes will be somewhat easier, especially if you learn Spanish before French.
Think of the relation between both like the relation of English to German. There is a similarity, but the languages are far from mutually intelligible.
As mentioned by others, "similarity" of two languages is a difficult thing to define. How do we start? Using a theoretical linguistics as discrete components to compare might be a good place: Syntax, Phonology, Phonetics, Morphology, and Semantics.
Let's pretend for now I am just comparing two made up languages,
Language A and
If we use a generativist model with Context-Free Grammars which are usually the ones taught in University (at least in North-America), we can look at Categorical heads and see how many have the "same configuration".
Are Noun-Phrases `NP`s head first or head last? Are Adjectival-Phrases `AP`s head first or head last?
This is dependent on the categorical models you use and how they are defined, but each time they are the "same configuration", we can tally it up and save the results (say 10/30 categories have the same configuration).
Simple phonetic sounds such as allophones and phonemes could be compared by existence alone. If each language shares one, we tally them up and save the results (say 30/65 sounds exist in both languages compared)
We can use triphones in some preexisting speech corpus and make a set of them. We can then tally up how many are shared in each language (let's say 763/900)
One could use just the phonological example I gave and say that the triphones capture similar sound sequences. Otherwise we can just count the times certain affixes exist in both languages and tally them up (let's just say 25/55 for this one)
Well, this is probably a very difficult one, as semantic similarity can be defined in many ways. It usually entails using corpora and counts of contexts, or using a specialized metalanguage for capturing semantic concepts.
We could also just say, well, both languages have the ability to explain the same ideas so they are basically the same and their difference is negligible (i.e. tallied up similarities would be the same amount).
After we figure out how to get the similarities, we can just average the results for our made up languages
Language A and
So using the examples I gave:
- Syntax: 10/30 = 33%
- Phonetics: 30/65 = 46%
- Phonology: 763/900 = 85%
- Morphology: 25/55 = 45%
- Semantics: 100/100 = 100% Same
Average similarity between made up languages
Language A and
(33+46+85+45+100)/5 = 61% the same
Basically, we would have to do the same thing for Spanish and French. We have lot's of data on the languages to we might be able to do it.
If we only care about one area, it might be easier, such as sounds (phonology, phonetics, morphology) or grammar (syntax)
This questions can be really subjective too so, depending on how people pick important features to compare. Also "same configuration" could be different for different people who study different aspect of Linguistics (physcholinguistics, syntacticians, phoneticians, computational linguists :) )
Spanish and French are similar in syntax and close in vocabulary due to their latin origin, but they are very different in sound because standard French has a celtic substrat and a germanic superstrat. Since Spanish has a fairly conservative sound system and French has a very conservative orthography, that means that written Spanish is somewhat similar to written French, the grammar will look familiar to you. However, spoken French is incomprehensible to somebody who only speaks Spanish, since the French sound system is totally alien to Spanish and much more complex.