English will follow

Je trouve que ce site internet est particulièrement bon pour ce que vous demandez. Il permet d’avoir accès à la traduction la plus probable dans la colonne de gauche, mais aussi et surtout à un panel d’extraits de textes traduits, ce qui est parfait pour avoir une bonne idée du contexte dans lequel l’expression est utilisée.

I find this website quite helpful as it gives you the most probable traduction options in the left column and puts them in the context of translated texts. The good thing is you can see both of the versions and it also works for other languages!

EDIT: back in 2014 Deepl wasn’t out. Go for Deepl, I use it all the time.

Old answer:
I usually use reverso to translate.
As you can see in this link, when I translate devis into English, I have a lot of synonyms and context at the bottom.
When I translate it on linguee I can’t find as much information without analysing all the sentences.

Online translator is a business, and it’s a matter of preferences. I just strongly recommend to NOT use google translate.

Yes, there are. You can look for them here: http://alternativeto.net/software/google-translate/

I recommend Babel Fish translator, but there are a number of others as well.

http://www.bonpatron.com is a good resource for grammar correction. It won’t translate for you, but it will fix your mistakes.

I am amazed at the realistic translations of DeepL.

And I think—just my impression—they are not wildly gathering data as google does.

Translations Comparison

Judge yourselves. I translated my own sentence above 😉

• DeepL

Je suis étonné par les traductions réalistes de DeepL.

Et je pense – c’est juste mon impression – qu’elles ne collectent pas
les données de manière aussi sauvage que le fait Google.

• Google Translate

Je suis étonné des traductions réalistes de DeepL.

Et je pense – juste mon impression – qu’ils ne collectent pas de
manière extravagante des données comme le fait Google.

…for finding the definitions of individual words. However, when it comes to learning about piecing together French phrases…

I understand it’s useful to have an interface where you can click words and have their definition appear below but this is not what those tools are about. You could focus on things you don’t understand and look them up in Wiktionary for instance; you can find an entry on the English side of things as well as the French-language page for the same item in more depth with pronunciation, sentences etc.. (see link on the left handside/bottom of the page). On Linux it’s most likely not difficult to build a little script which invokes content from such as website upon pasting content to the terminal etc.

You can use spaced learning flashcard-like based training to expose yourself to sentences. And you can read some specific grammar guidelines in context from different training resources or formal material to shape your understanding of usage from a more abstract perspective. Learning phrases and different constructs and making sentences out of these takes time but in my opinion you should look into specific things you want to say, focusing on the significant part of speech you’re interesting in, and read sentences and try to make it happen and ask specific questions about the challenges you face.

As for translation engines, they sometimes do fine at first glance, some feel more crowdsourced than others, but that’s just a false sense of security. Take for instance the translation from DeepL found in some other answer ; it totally fails when it uses the "elles" pronoun, as it’s not the translations (feminine plural) which do the collecting but rather the people at Google, "les gens chez Google", so for me what would be natural here is "ils". So the translation lost track of pronoun assignments on a return carriage ; it doesn’t know what it’s talking about. Furthermore most likely you meant "autant" or "aussi librement" with "wildly" and there is no need to boost the adjectival value of that imho.

Wordreference is very good too!