Marie mène le projet avec détermination.

Mène is the third-person singular present form of the verb mener, which means to lead, to run, or to manage depending on context.

The grave accent in mène is part of a spelling change that helps show pronunciation. In forms where the syllable with e is followed by another syllable containing a silent e, é in mener often changes to è:

• je mène
• tu mènes
• il / elle mène

But:

• nous menons
• vous menez

So Marie mène means Marie leads / is leading.

Mène is pronounced roughly like men in English, but with a clear French vowel and no strong English-style diphthong.

A simple approximation is:

• mène ≈ men

The important part is that è sounds more open than é. So:

• é in mener sounds more like ay
• è in mène sounds more like eh

In this sentence, le projet means the project and is the direct object of the verb mène.

French usually uses an article where English sometimes does too, and here the definite article is needed because we are talking about a specific project:

• Marie mène le projet. = Marie is leading the project.

If you said un projet, it would mean a project:

• Marie mène un projet. = Marie is leading a project.

Du projet would not fit here as the direct object in this meaning.

Yes, this sentence follows the basic French word order:

• Subject + verb + object

So:

• Marie = subject
• mène = verb
• le projet = direct object

This is very similar to English:

• Marie leads the project.

Then the phrase avec détermination adds extra information about how she does it.

Avec détermination is a prepositional phrase meaning with determination. It explains how Marie is leading the project.

Breakdown:

• avec = with
• détermination = determination

So the sentence structure is:

• Marie — subject
• mène le projet — main action
• avec détermination — manner / attitude

It works a lot like English with determination.

Yes. French could use an adverb such as déterminément in some contexts, but that is much less natural here. The phrase avec détermination is the normal, idiomatic choice.

Compare:

• Marie mène le projet avec détermination. = very natural
• Marie mène le projet d’une manière déterminée. = possible, but heavier
• Marie mène le projet déterminément. = not the usual way to say this

So for learners, avec + noun is a very common and useful pattern.

Not exactly, though they can overlap.

• mener often means to lead, to carry forward, to conduct, or to run
• diriger often means to direct, to be in charge of, or to manage

In this sentence, mène le projet suggests Marie is actively leading the project forward.
If you said Marie dirige le projet, that would also be possible, but it may sound slightly more like she is the official manager or director of it.

So:

• mener un projet = to lead / carry out / run a project
• diriger un projet = to direct / manage a project

The noun is la détermination, so it is feminine because that is simply its grammatical gender in French.

Many abstract nouns ending in -tion are feminine:

• la détermination
• la direction
• la situation
• la décision

Even though the article does not appear here after avec, the noun still has its grammatical gender. You would see it if you used an article:

• avec une grande détermination

After avec, French sometimes uses a noun without an article, especially in fixed or very natural expressions describing manner.

So:

• avec détermination = with determination

This is idiomatic and perfectly natural.

You may also see:

• avec de la détermination
• avec une grande détermination

These are possible, but they are slightly different in feel:

• avec détermination = general manner
• avec de la détermination = with some determination / showing determination
• avec une grande détermination = with great determination

Yes. Mène is in the present tense.

Like the French present tense in general, it can often translate as either:

• Marie leads the project
• Marie is leading the project

French uses the same simple present form for both ideas, and context tells you which English translation sounds best.

Yes. Projet is a broad word. It can mean:

• a work project
• a plan
• a proposal
• a personal project
• an undertaking

So le projet here could refer to many kinds of projects, depending on context.

To make it negative, put ne ... pas around the conjugated verb:

• Marie ne mène pas le projet avec détermination.

That means:

• Marie is not leading the project with determination.

If spoken in informal French, ne is often dropped in conversation:

• Marie mène pas le projet avec détermination.

But in standard written French, keep ne ... pas.

There are several common ways:

• Marie mène le projet avec détermination ?
  Rising intonation in speech

• Est-ce que Marie mène le projet avec détermination ?
  Very common and natural

• Marie mène-t-elle le projet avec détermination ?
  More formal inversion

All three mean:

• Is Marie leading the project with determination?

Usually, conduire is not the best choice here.

Conduire most commonly means:

• to drive
• to lead someone somewhere
• to conduct in some contexts

For a project, French much more naturally says:

• mener un projet
• diriger un projet
• gérer un projet depending on the exact meaning

So for this sentence, mène le projet is the most natural phrasing.